Well okay. "Blue" is a stretch. Though a few genuinely blue plants are rumored to exist (Micorsorum steerii, an unknown Begonia species), one, they're iridescent, and change color depending on the angle at which they're being viewed, and two, it'd be a stretch to call them houseplants, since the Begonia isn't even in cultivation as far as I know, and the Microsorum is cultivated but not really suitable for the home outside of a terrarium. And maybe not inside a terrarium, either. I don't know anyone who's tried.
But there are still plants out there with some blue to them. Most are succulents, and the blue coloring is the result of a fine, powdery layer of wax covering the leaves and/or stems, which is confusingly called "bloom." The main purpose of bloom is to reflect excess light (especially ultraviolet) and heat away from the plant, which is why it's common on desert plants, but it also, being wax, is water-repellent, so other kinds of plants find uses for it as well (for example: the leaves of some varieties of cabbage; the leaves, stems, and seed pods of poppies; fruits of grapes and certain other fruits).
Because bloom serves a self-shading purpose in a lot of the plants in which it is found, plants grown indoors may not produce as much, and may as a result appear more green than plants of the same type grown outdoors. Bloom also rubs off easily when plants are handled, so if you value the color, try to touch the leaves as little as possible. On the other hand, some plants may change color if they're in very bright light (such as full sun outdoors): many Aloes, for example, will turn red or brown-red in full sun. Others will stay blue or green but will get reddish leaf margins.
Because there's no good way to define "blue" for these purposes, and because plants grown in different conditions may look different, I don't guarantee that you'll agree with my choices here, but I did search davesgarden.com for "blue," all 75 pages of results, so I'm trying to cast a wide net. (I also got to look at a ton of purple daylilies and potatoes, which makes me think that hort types have a broad and flexible understanding of the meaning of the word "blue" anyway.) Please note also that I'm excluding plants with blue flowers from consideration: here we're only thinking about leaves and stems. If I can come up with ten houseplants with blue flowers, and that's a big if, then blue-flowering plants will get their own list someday.
Aloe brevifolia. In outdoor sun, plants have a tendency to turn different colors: depending on the photo, they may be bronze, purple, or gray. My plant doesn't get much direct sun, and it has been light blue-green pretty much the whole time I've had it.
Browningia hertlingiana. Photos show variable color, but from what I can tell, the color tends to be a pretty solid turquoise/blue.
Echeveria cvv. (some cvv.) The blue cultivars tend to be a fairly pale, washed-out, greenish-blue, often with pink or red leaf tips.
Juniperus sp. Variable color depending on species, photography, and culture, but I think it's close enough to count.
Melocactus azureus. Quite a few pictures that turned up in Google image search looked pretty plain green, no blue at all, but the one in this picture really was as blue as shown. I assume either cultural differences or misidentifications.
Myrtillocactus geometrizans. The picture does a terrible, terrible job of illustrating the color (though it does show how the bloom rubs off with handling), but Myrtillocactus is typically a vivid blue-green.
Phlebodium aureum 'Mandianum.' New fronds in particular tend to be a dull blue-gray. My personal plant is a lot more yellow-green now than it was when I bought it, probably because of inadequate light, but the new fronds still emerge bluish.
Sedum morganianum. Plants kept in insufficient light will be greener. The real color is less saturated than that in the photo.
Selaginella uncinata. The blue color is due to iridescence. I don't know what these do in lower light.
On the do/don't recommends:
I do recommend Agave 'Blue Glow,' which has done fine for me so far under lights in the basement. It's unclear whether it's going to be a particularly good long-term indoor plant, and I'm aware they can get very large, which is a worry, but so far, so good.
Sedum morganianum is a favorite plant of mine: I was worried, after Sedum x rubrotinctum always seemed to be reaching for more light, that I wouldn't be able to grow S. morganianum, but my plant has been in a west window since the move, and it's been one of my better-behaved plants. It does drop leaves every time I water it: they're loosely attached to the stem, and come off easily. After trying for a while to prevent this from happening, I've decided to just accept that it will, and start new plants with the leaves that come off. As a result, we currently live with five pots of Sedum morganianum, and I expect there will be more coming along all the time.
The third recommend is Aloe brevifolia. It's not my most exciting plant, but it's been steady and unproblematic, and I've had it for a very long time (relatively speaking), so it wins out over the various plants in this list that I haven't had for very long or that haven't done much of anything (Browningia, Myrtillocactus, Phlebodium) or the nice-seeming plant I've never had at all (Melocactus).
For the un-recommend, I'm torn between Juniperus and Selaginella. Both are pretty inappropriate for your average indoor houseplant-grower, though for different reasons: Juniperus wants cooler temperatures, especially during the winter, and Selaginella is unforgiving of missed waterings and dry air. I suppose most people who received both at once would kill the Selaginella first, so if I have to choose, then Selaginella is the anti-recommend.
- Several other Agave species and hybrids are blue to some degree or another; I'm particularly fond of the plant I think might be A. desmettiana.
- Many, many Aloe species and hybrids, including A. 'Blue Elf,' A. maculata, A. striata, A. vera, and A. 'Walmsley's Blue,' are bluish-green.
- Bismarckia nobilis is perhaps a little large and demanding to work as an indoor plant, but I've heard of people making the attempt, and it's sort of a silvery-blue in good conditions.
- Cereus aethiops varies a great deal in photos, but looks like it tends to be somewhere in the blue/green part of the spectrum most of the time.
- Chamaedorea cataractum, when grown in good conditions, has a metallic blue sheen to some of the fronds, though I expect that fades when grown indoors.
- Chamaedorea metallica has a sort of dull blue-gray color under some conditions.
- I'm not sure it makes a great houseplant, but the blue Mediterranean fan palm, Chamaerops humilis var. argentea, shows up as silvery blue in some photos.
- Crassula arborescens var. undulatifolia (sometimes sold as C. 'Blue Bird') is slightly bluish under strong light, and plain green under lower light.
- Also maybe not great houseplants: Cycas angulata (silvery-blue) and C. ophiolitica (slightly bluish green). The related cycads Encephalartos arenarius (highly variable, according to the pictures: olive green, blue-green, silvery) and E. horridus (much more uniformly silver-gray, with hints of blue) would also technically qualify.
- Dasylirion berlandieri and D. wheeleri are both bluish-gray, and I've seen D. wheeleri, at least, sold as a houseplant. No idea how well that works out for people.
- Echinocactus horizonthalonius is a dull, mostly gray shade of blue under some conditions.
- I'm not sure I believe in the existence of Epipremnum aureum 'Cebu Blue' or not, and if it does exist, I'm not sure it qualifies as blue except in name. Can't tell much from the photos.
- A number of Ferocactus spp. are blue or grayish-blue.
- Haworthia limifolia var. ubomboensis is mostly green, but with a hint of blue or blue-gray, depending on conditions and photography. A few other Haworthia species are also sometimes bluish, though they tend to be green or gray.
- Kalanchoe eriophylla is, according to davesgarden.com, given the common name of "Blue Kalanchoe," though it's more white than anything -- I'm not sure I see it.
- The younger leaves of Kalanchoe luciae and K. thyrsiflora are covered with a light bluish bloom, though it's temporary and not particularly intense.
- Kalanchoe marmorata is bluish-green or bluish-gray in good light.
- Kalanchoe tomentosa varies according to photography and growing conditions, but are sometimes gray-blue or blue-green.
- I found it a very disappointing houseplant, but Lamprathus blandus has lots of oddly-shaped leaves that can appear as blue, green, gray, or intermediate shades thereof.
- Leuchtenbergia principis is a bizarre cactus with blue-gray projections which resemble leaves. In strong light, the "leaves" will be edged with reddish-purple.
- Several cultivated Lithops varieties are blue-green or blue-gray.
- Microsorum steerii and M. thailandicum are both apparently a striking, deep, iridescent blue/green/black; whether they can be grown indoors is questionable.
- Several Opuntia species are blue-green, blue-gray, or blue-violet at certain points in the year, though since the most dramatic color is brought about by cold, a plant raised indoors year-round is unlikely to exhibit the full range of color.
- Some cultivars of Pachyphytum, xPachyveria, and xGraptoveria are blue, gray, or violet to some degree or another.
- Davesgarden.com lists a Peperomia 'Blue Whale,' which the photos make look mostly black, but I suppose it could plausibly be blue.
- Pilosocereus pachycladus is a washed-out bluish-gray.
- Sedum burrito is very similar to S. morganianum, pictured above, though the leaves are more rounded and are more perpendicular to the stem.
- Senecio crassissimus has red-edged blue-gray leaves when grown in bright enough light.
- I've never seen Senecio serpens and S. talinoides attempted indoors, but we did keep an S. talinoides (I think) in the greenhouse over a winter at work, and it grew okay. Possibly you'd have to use supplemental lighting. Both are powdery blue or blue-gray.