The usual disclaimers apply, but let's run through them again just to make sure we're all on the same page:
1) This is not an exhaustive list of red-flowering houseplants; I'm not sure it's even possible to come up with an exhaustive list of red-flowering houseplants. And if it were possible, it probably wouldn't be desirable. This is plenty long as it is.
2) Also, many of the plants on the list are available in multiple cultivars, not all of which necessarily bloom red.
3) I'm approaching these lists from an interior-decorating standpoint, not a botanical one. If the plant has showy red bracts with tiny yellow true flowers, I'm counting it as a red-bloomer, because that's how most people would think of it.
4) As there are no sharp dividing lines between "red," "orange," "pink," and "purple," you may disagree with me about the redness of some of the flowers mentioned here. Which if it's all the same to you, I'm going to see that as more your problem than it is mine.
5) In some cases, I'm going wholly or partly by the results from Google image search for the plants in question. Since people sometimes post misidentified pictures, there is a small chance that some of the plants listed, especially more obscure plants, may be included in error.
Clerodendrum x speciosum. (C. splendens x C. thomsoniae)
Cyclamen persicum NOID.
Episcia 'Silver Skies.'
Hatiora (formerly Rhipsalidopsis) NOID.
Kalanchoe blossfeldiana NOID.
Parodia microsperma. Some other Parodias have red flowers as well, though yellow is more typical.
This is a tough list to do recommends / anti-recommends for: for all of these, I either have 1) no experience, 2) exclusively bad experiences, or 3) very mixed experiences. If forced to come up with something, though, I would reluctantly recommend Aeschynanthus, Episcia, and Neoregelia.
My personal experience with Aeschynanthus lobbianus was mostly negative, but I don't think it was the plant's fault: I should have kept up better with the watering. Other Aeschynanthus species have done well for me, enough so that I'd feel comfortable recommending them to other people. The main obstacles to cultivation are light (they need at least bright indirect light, and I'd highly recommend at least some direct sun) and temperature (always above 60F/16C).
I enjoy Episcias, but varieties either tend to do really well for me ('Coco,' 'Suomi,' several NOIDs, 'Faded Jade,' 'Raspberry Parade') or really poorly ('Pink Acajou,' 'Kempenfest,' 'Burning Embers'), without much of a middle ground. 'Silver Skies' is one of the good ones, though it's a bit slower than the others, and stays smaller. Main obstacles to cultivation: temperature (always at least 60F/16C), water (don't let them dry out to the point of wilting) and humidity (higher is better).
I was a huge fan of Neoregelia at one point a few years back; I've cooled off on them somewhat since then, for various reasons, but they're perfectly fine plants if you have the space for them and don't mind getting caught on their sharp marginal spines occasionally. Biggest obstacle: light (at least bright indirect, with some direct sun strongly recommended).
For the anti-recommend, I guess I'll go with Hibiscus, though Cyclamen and Kalanchoe were really close. They all can be grown indoors successfully, but none are particularly well-suited to it. Cyclamen goes in and out of dormancy at erratic intervals and is easily overwatered as a result; Kalanchoe virtually always goes downhill once purchased, because it needs extremely bright light.
Hibiscus has both problems: it defoliates in the winter, to a greater or lesser degree depending on how it's treated, and it's very difficult to rebloom in the house if you don't have a lot of light. (Though it's easier than Kalanchoe.) Hibiscus has one problem that the other two don't, though, which is that they're incredibly appealing to pests. At work, we were always wrestling with spider mites, whitefly, and aphids; I've also had spider mites on plants at home. Hibiscus are gorgeous, obviously, but it's just not worth the hassle to bring them inside for the winter. People with huge windows or small plant collections might find Hibiscus more rewarding than I do.
- Some Abutilon cvv.
- Acalypha reptans. (pinkish-red)
- Acalypha wilkesiana. (not particularly ornamental; pink-red; small)
- Some Adenium cvv.
- Some Aechmea spp./cvv. (bracts)
- Ananas comosus. (bracts; pink-red; true flowers are blue-purple)
- Some Anthurium hybrids are true red.
- Ascocenda Sweet Pea 'Ruby.' (pinkish red)
- Austrocylindropuntia subulata. (variable, ranges from orange-red to pink; usually closer to pink)
- Some Begonia cvv. (usually more pink or pink-red, though Reigers, wax, and tuberous begonias can all have true red flowers)
- Some Billbergia spp./cvv. have flower stalks with red bracts, though pink is more common. The true flowers are generally some combination of blue, green, and white.
- Some Bougainvillea cvv.
- Bryophyllum daigremontianum.
- Bryophyllum tubiflorum. (orange-red)
- Calliandra emarginata. (pink-red; possibly not actually a houseplant)
- A few orchids in the Cattleya alliance produce flowers that are red to some degree or another; two of the more striking examples are Laeliocattleya Rojo x Cattleya aurantiaca (picture) and Lyonara cv. (Schomburgkia undulata x Sophrolaeliocattleya Rojo) (picture)
- Clerodendrum thomsoniae. (white bracts / red flowers)
- Some Columnea cvv./spp. might qualify, though usually they're more orange or orange-red than red.
- Crassula falcata.
- Dischidia pectinoides. (true red to pink-red; small)
- Echeveria coccinea (red or orange-red; see post) and some other Echeveria cvv. (They're usually pink or orange-pink with a yellow rim/tip, though.)
- Epidendrum Max Valley (orange-red) and some other Epidendrum cvv.
- Some Epiphyllum cvv.
- Some Euphorbia milii cvv.
- Some Euphorbia pulcherrima cvv., though I would never recommend that anybody get a Euphorbia pulcherrima.
- Some Ferocactus spp./cvv.
- Graptopetalum bellum. (pink-red; I don't know if this is cultivated often enough to count for the list)
- Graptopetalum pentandrum var. superbum. (also sometimes called G. superbum; brick red at petal tips)
- Several Guzmania cvv. have red, purple-red, or orange-red bracts.
- Some Heliconia spp./cvv., though I'm not sure Heliconia should qualify as houseplants.
- The spathe of Homalomena 'Perma Press' is red (link). It's arguably not a houseplant either (too big), even though I'm growing it as one.
- Hoya DS-70. (variable: dark red, orange-red, pink, pink-red)
- Hoya polyneura. (dark red / pink-red / purple-red, with white)
- Hoya pubicalyx. (dark red)
- Several Huernia species have red flowers to some degree or another, usually very dark maroon or burgundy. These include: Huernia aspera (dark red), Huernia confusa (dark red), Huernia guttata (dark red), Huernia insigniflora (large red annulus1 on peach petals), Huernia keniensis (flowers are white or pale yellow with a very dark red interior), Huernia leachii (dark red stripes on pale yellow), Huernia oculata (very, very dark red petals around a central bright white circle; I didn't know about it before this post, but now I want one really badly), Huernia piercii (dark red spots on white), Huernia plowesii (dark red annulus with dark red spots elsewhere), Huernia procumbens (dark red), Huernia schneideriana (dark red), Huernia transvaalensis (dark red annulus), Huernia zebrina (usually dark red annulus, plus dark red stripes on yellow petals, but color varies).
- Justicia carnea (true red) and Justicia spicigera (orange-red). Some Justicia species are grown as houseplants, though I don't know whether J. carnea or J. spicigera are among them to a meaningful degree.
- Kalanchoe tomentosa flowers are hard to describe. See the pictures at this link.
- Some (most?) Kohleria cvv.
- Loropetalum chinensis? (pink-red; uncertain about its suitability as a houseplant)
- Some Mammillaria spp. have pink-red flowers, though they're typically much closer to pink than to red.
- Some Mandevilla cvv. (link)
- Masdevallia schlimii (color varies in photos: brick red, dark orange-red, dark purple-red)
- Maxillaria tenuifolia maybe barely qualifies as red. (dark red-brown)
- Some Miltoniopsis cvv., arguably. (tend to be more pink-red or purple-red than true red)
- Some Musa spp. have some red in their inflorescences, though it isn't usually the main color. Ensete ventricosum has an inflorescence which is primarily dark red.
- The central leaves of several Neoregelias will flush red at the center when blooming, though the actual flowers are usually lavender or blue-purple.
- Some Nerium oleander cvv. (pink-red; suitability as a houseplant is questionable)
- Some orchids in the Oncidium alliance, though there doesn't seem to be a lot of true red: most lean toward either brown or pink. Some of the closer ones: Burrageara Nelly Isler (link; pinkish), Miltassia Charles M. Fitch x Odontocidium Black Beauty link; very dark red), Vuylstekeara Aloha Sparks 'Ruby Eyes' (link; washed-out and orange-red), Wilsonara Lisa Devos (link; brick red and pink), Oncidium Sharry Baby (link; dark red), Miltonidium Bartley Schwartz 'Highlander' (link; dark pink-red)
- A few Opuntia spp./cvv. flowers are red or orange-red, including O. aciculata and O. bergeriana. O. 'Claude Arno' is a dark violet-red.
- Pachira aquatica is not likely to bloom indoors, but the flower has yellow reflexed petals with lots of long, white, red-tipped stamens. You wouldn't look at it and say "now there's a red flower," but there's definitely quite a bit of red involved.
- At least one Pachyphytum sp. or cv. has flowers with dark red interiors, though I don't know which one and it doesn't appear to be typical for the genus.
- Pachypodium baronii has solid-colored, true red flowers; P. namaquanum has yellow flowers with petals that don't open very wide and are red-brown at the tips. All other Pachypodium spp., including the most commonly-grown ones, have white, yellow, or pink flowers.
- A few Pachyveria hybrids have flowers that look reddish in pictures, though pink, yellow, and green are more common.
- Phragmipedium orchids get close to true red once in a while. Closest two I've personally run into were Phragmipedium Sargent Eric 'Timberlane' (pretty true red; a bit orangey) and Phragmipedium Fox Valley 'Fireball' (pretty close to true red, a little pinkish).
- Pedilanthus tithymaloides. (unlikely to bloom indoors)
- Some Pelargonium x hortorum cvv. are true red or dark red.
- Pereskia bleo are either orange-red or red, according to photos; Pereskia flowers are more typically pink/lavender. I don't know P. bleo's suitability for indoor culture, though at least one Pereskia (P. aculeata) does well indoors.
- A few Phalaenopsis orchids tend toward something like red, though I have yet to see any true red phals.
- A handful of Philodendrons produce inflorescences with solid red spathes; the most commonly sold is P. 'Moonlight,' but the species P. eichleri also does. The spathes of P. martianum (aka P. cannifolium) are white with a dark red base.
- A few Pinguicula spp. have true-red flowers, most prominently P. laueana. Maybe also P. caryophyllacea?
- Some Rhododendron cvv. are brilliant true red, though I would argue that they're not houseplants.
- Some Saintpaulia cvv. are dark red or pink-red; I have yet to see true red.
- Salvia elegans.
- Schefflera actinophylla. (dark red, very unlikely indoors)
- Several Schlumbergera cvv. are vivdly red.
- Sedum burrito. (rare; variously pink, coral, or pink-red)
- Sedum morganianum. (rare; photographs show true red, red-orange, dull red, dark red)
- Sempervivum cvv./spp. flowers are typically (but not always) dull red or pink-red.
- Some Sinningia cvv./spp.
- Most Stapelia flowers involve dark red or dark purple-red somewhere, though it's never a particularly vibrant red, and not very many of the flowers give an overall impression of red. Most notable exceptions: Stapelia cedrimontana is black-red with red and yellow stripes near the center; Stapelia hirsuta has very dark red stripes on a peach background, giving the overall impression of dark red; Stapelia leendertziae -- which I also covet -- is solid dark red or dark purple.
- Stenorrhynchos speciosum.
- Stenosarcos Vanguard 'Fireball.' (pink-red)
- Some Streptocarpus cvv. (pink-red)
- Stromanthe sanguinea cvv. (red or pink-red; unlikely to happen indoors)
- Synadenium grantii. (dull dark red, small, unlikely indoors)
- Many Vriesea hybrids, and some of the species (notably V. splendens) produce inflorescences with red bracts.
As usual, I am totally open to it if readers want to make additional suggestions in the comments.