Lots and lots of caveats for this one.
1. I could be mistaken. I've collected what appears to be good information from knowledgeable sources, but they could be wrong, I could have been looking at the wrong line on the page, etc.
2. You might not have the identity of your plant correct, even if I do.
3. Just because some part of the plant may be edible, it does not necessarily follow that the rest of the plant is safe to eat.
4. Even if you and I have both identified the plant correctly and I have good information regarding the edibility, some "edible" plants are poisonous if not prepared in a certain way. Some things have to be cooked first. Some things have to be washed and filtered and washed again, and so forth. Some fruits are incredibly nasty if you try to eat them before they're ripe. And so forth. So don't just assume you know how to prepare it.
5. Even if I'm right about the identity of the plant, and you're right about the identity of the plant, and I've located good information about which parts are edible and under what circumstances, and you prepare the plant properly, if the plant hasn't been in your care for a reasonably long time, it may still have been sprayed with pesticides of some kind and be unfit to eat. Unless you know where it's been, don't assume you can eat it.
6. I also have to qualify this list by adding "in theory" and "someday." In general, tropical houseplants need to be fairly old, large, and healthy before they will flower and fruit, which is fairly difficult to pull off in normal home conditions. One stands a better chance, obviously, with leaves.
7. Even if you manage to get a plant to the point where it bears fruit indoors, or whatever, and you know for sure what plant it is, and I've identified it correctly, and I was working from good information, and you prepare it correctly, and it's been yours for long enough that pesticides aren't a problem, you may find that the fruit (or whatever), when eaten, is not particularly good, compared to the sorts of stuff you could get from the supermarket.
8. And you could be unlucky enough to have an allergic reaction to the plant anyway.
But! Hypothetically! If you were locked in a tropical botanical garden or garden center greenhouse full of houseplants or whatever, and aliens/zombies/genetically-engineered frog-bear hybrids/H1N1 flu/bird flu/Big-Bird Flu1/whatever attacked Earth and killed everybody except for you, these are the plants that could maybe keep you going for a few more miserable weeks as you starved to death, dazed by grief and shock and completely alone. I think I personally would get the hell out of the botanical garden and set up in a nice abandoned supermarket somewhere, with a can opener, charcoal grill, and a few blow-up dolls or mannequins for company, but hey. It's your apocalypse; you do what you like.
Of the above, the three I'd recommend would be Cereus peruvianus, Myrtillocactus geometrizans, and Coffea arabica. Cereus is definitely a pretty nice guy, and although I don't know Myrtillocactus as well, it seems friendly enough so far, and the fruit is supposed to resemble blueberries. Even if it's a long shot, that's still pretty cool. Also the color is nice -- the photo makes it look more green than blue, but in person it's more blue than green.
Coffea arabica is a weird one to recommend, since it's supposed to be a fairly difficult plant. Monstera deliciosa would be the more obvious choice for the third recommend. But, if I'm honest with myself, my Coffea has done better here than my Monsteras have. So Coffea it is.
The anti-recommend would be Opuntia microdasys, because of the glochids (tiny barbed hairs that get embedded in skin and itch and hurt -- they're terrible). I think Opuntia microdasys is actually the very species of Opuntia that traumatized me as a child in Evil Grandmother's house.
NOTE: Much of the below information was gathered from Plants for a Future. I'm reaching kind of hard for plants that qualify, but everything in the below list is either a plant I've grown indoors more or less successfully, or a plant I've heard of people growing indoors more or less successfully. Additional suggestions are welcome.•Abutilon cv. (Flowering maple) Edible portion: flowers. Leaves are technically edible but not very good.
•Agave americana, A. parryi, A. tequilana (Century plant, tequila agave) Edible portion: baked leaves, stem, and seeds; sap and fermented sap. Some people's skin is irritated by the sap. (Usually too large to be particularly good houseplants.)
•Aloe vera (Medicinal aloe) Edible portion: juice from center of leaves. Avoid juice from near the leaf surface if you like the current speed of your digestive system.
•Amaranthus caudatus (Love-lies-bleeding) Edible portion: leaves, seeds. (from comments; not common as houseplant)
•Aptenia cordifolia Edible portion: leaves. (from comments; uncommon as houseplant; likely harmful in large amounts)
•Araucaria araucana (Monkey-puzzle tree) Edible portion: seeds (fresh, cooked). (uncommon as houseplant)
•Araucaria bidwillii (Bunya-bunya) Edible portion: seeds (fresh, cooked, partly sprouted). (uncommon as houseplant)
•Asparagus setaceus (Asparagus fern) Edible portion: cooked young shoots. Apparently does not include the related A. sprengeri, though I'm not positive about that.
•Aucuba japonica (Spotted laurel, Japanese laurel) Edible portion: cooked leaves, but you'd have to be fairly desperate, from the sound of it.
•Calathea allouia (Sweet corn root) Edible portion: roots. (from comments; I've never actually heard of it being grown as a houseplant)
•Capsicum annuum and some other Capsicum spp. (Ornamental peppers, Sweet peppers) Edible portion: fruits.
•Some Caralluma spp. Edible portion: stems? I assume? Likely toxic in large quantity (from comments; uncommon as houseplant)
•Celosia argentea (Lagos spinach, Feather cockscomb) Edible portion: leaves. (from comments; I've never actually heard of anyone growing it as a houseplant)
•Chamaerops humilis (Dwarf fan palm) Edible portion: young leaf buds or suckers, fruit. (uncommon as houseplant)
•Citrus sinensis (Orange), C. limon (Lemon), other Citrus, Citrofortunella, and Fortunella spp. Edible portion: fruit, flowers.
•Dasylirion wheeleri and other Dasylirion spp. (Sotol) Edible portion: cooked or fermented stem, flowering stem. (I've seen it sold as a houseplant, but I don't know anyone who's actually grown it successfully indoors.)
•Ensete ventricosum (Ornamental banana?) Edible portion: rhizomes. (from comments)
•Epiphyllum anguligar Edible portion: fruits. (from comments)
•Some Ficus fruit, but not the species ordinarily cultivated indoors.
•Hibiscus rosa-sinensis (Tropical hibiscus) Edible portion: flowers, young leaves (?). Root is technically edible but not very good.
•Hydrocotyle leucocephala (Brazilian pennywort) Edible portion: leaves. (from comments; uncommon as houseplant but maybe semi-common as aquarium plant)
•Ipomoea batatas (Sweet potato) Edible portion: tuber. Uncommon as houseplant, though some ornamental varieties are widely grown outdoors.
•Laurus nobilis (Bay tree) Edible portion: leaves (fresh or dried), fruit, flowers.
•Liriope spicata (Lilyturf) Edible portion: cooked roots. (Rare as houseplant, though I'm growing the variety 'Cassidy' inside now. It's going so-so.)
•Maranta arudinacea (Arrowroot) Edible portion: tubers. (from comments; I've never actually heard of it being grown as a houseplant)
•Muehlenbeckia complexa (maidenhair vine) Edible portion: "fruit" (actually swollen flowers). (uncommon as houseplant but not unheard of)
•Ocimum basilicum (Basil) Edible portion: leaves.
•Olea europaea (Olive tree) Edible portion: fruit.
•Ophiopogon japonicus (Snake's beard) Edible portion: root. (Rare as houseplant, though I'm growing O. planiscapus var. nigrescens indoors now. It's not particularly satisfying: growth is slow.)
•Origanum majoranum (Marjoram) and O. vulgare (Oregano) Edible portion: leaves.
•Oxalis deppei (Iron cross oxalis) Edible portion: leaves, flowers, root. Excessive consumption can lead to calcium deficiency and other problems.
•Oxalis stricta (Yellow wood sorrel) As for O. deppei. It's a common enough hitchhiker in houseplants (around here, anyway) that I figure it qualifies as a houseplant, though it's rarely (never?) cultivated indoors on purpose.
•Oxalis triangularis (False shamrock, purple shamrock) As for O. deppei.
•Pachira aquatica (Money tree, Water chestnut, Malabar chestnut) Edible portion: nuts, leaves, flowers. (from comments)
•Passiflora spp. (Passion flower, Passion fruit) Edible portion: fruit. (from comments)
•Perilla frutescens (Perilla, Shiso, Beefsteak plant, Purple mint, Japanese basil) Edible portion: leaves. (from comments)
•Persea americana (Avocado) Edible portion: fruit.
•Portulacaria afra (Elephant bush, Spekboom) Edible portion: leaves.
•Rosmarinus officinalis (Rosemary) Edible portion: leaves. (I know people grow it indoors, but I don't recommend it.)
•Salvia elegans (Pineapple sage) Edible portion: leaves. (uncommon as houseplant, but undeservedly so)
•Salvia officinalis (Sage) Edible portion: leaves. Can be toxic when used to excess and/or over long periods.
•Saxifraga stolonifera (Strawberry begonia) Edible portion: leaves, flowering stem. Usually cooked.
•Sempervivum tectorum (Houseleek) but not necessarily other Sempervivum spp. Edible portion: young leaves and shoots. (much better as an outdoor plant than an indoor one, in my experience)
•Solanum lycopersicon (Tomato) Edible portion: fruit. (from comments; uncommon as houseplant)
•Stevia rebaudiana (Stevia) Edible portion: leaves.
•Thymus vulgaris (Thyme) Edible portion: leaves.
•Trachycarpus fortunei (Chusan palm, Chinese windmill palm) Edible portion: young flower buds (cooked).
•Tropaeolum majus (Nasturtium) Edible portion: leaves, flowers, seed, seedpod.
•many Yucca spp., including Y. guatemalensis, the only one commonly grown indoors. Edible portions: flowers, fruit, leaves, stems. (from comments)
•Zingiber officinale (Ginger) Edible portion: rhizome. (from comments; I'm told it's a fairly uncooperative houseplant)
1 ("Mr. Hooper's Revenge")