This article includes a lot of Latin names of plants. You can look these up in books in any language or find information from search engines.
Obviously no plant is completely indestructible but some come pretty close. Let's start by considering things that tend to kill plants:
Lack of water
Too much water
Lack of light
Too much light
To hot
To cold (particularly frost but some plants will die of cold when above freezing)
Lack of humidity
Excessive humidity
Wrong pH or soil composition
Pests
Diseases
Natural life expectancy some plants don't live long normally
Lack of a resting period
Neglect by owner
Excessive fussing by owner
Some plants are parasites and need an appropriate host but they're seldom cultivated. What plants are easy to grow will depend on your conditions and if you're inclined to neglect plants or overly fuss them. Many plants can survive neglect but I'm not aware of any which can survive excessive fussing. If fussing is your problem, I suggest you get a small pedigree dog or perhaps stick to arranging cut flowers. If you really must have live plants, then perhaps you should grow bonsai trees, which need frequent pruning or learn to propagate orchids by micropropagation or something.
Most the plants I'm listing are succulents. In part this is my personal area of expertise but most succulents have lack of water, bright light, hot conditions, low humidity and neglect licked, and some can cope with other things.
Agavaceae (basically Agave and Yucca) This family are mostly very easy to grow. They will survive drought, neglect, a wide range of lighting conditions, most pests don't seem to like them and most will take a fair amount of frost in some cases to the extent that they don't really count as houseplants. The main problems are their generally large size and that they seldom flower (some Agaves are monocarpic, meaning that they flower once and then die). Yuccas don't really look succulent for those who don't like succulents.
Amariliaceae (Amaryllises etc.) Heamanthus albiflos isn't a plant you see much. It forms clumps of large bulbs that grow above the soil and have a fan shaped arrangement of short leaves. It also has clusters of white flowers. Treat like an Aloe.
Aloaceae (basically Aloe, Gasteria and Haworthia) Most people don't realize that Aloe vera is only one species of the large and varied genus Aloe. Aloes vary from small, grass-like plants to sizeable trees with some shrubs and many large, short-stemmed rosette plants in between. The larger species are problematic as houseplants because of their size. Generally they're easy to grow, tolerating drought, neglect and a wide range of lighting conditions. Unlike the similar looking Agaves, they flower frequently once big enough (another reason to grow the small species) and none are monocarpic. However they mostly turn to mush at the first sign of frost. The hardiest and most indestructible is probably A. aristata, which also happens to be one of the smaller species. Gasterias and Haworthias differ from Aloes by their flower structures. They're also mostly easy to grow and similar cultural requirements to Aloes but even the biggest ones are sensible houseplant sizes.
Araceae (Philodendron family)- I don't know much about these as there is only one succulent member (Zamicaulos zamifolia). Many of them are easy to grow and like shady (tolerating more shade than most houseplants), web conditions.
Cactaceae (true cacti many genera) This is a huge family. Most like dry, brightly lit conditions and warm temperatures, at least in the summer. Their ease of cultivation varies from nearly indestructible to pretty much impossible to grow. It's probably a good idea to divide this family into several groups.
Pereskioideae only one genus, Pereskia, which few people have much experience of growing. They're large shrubs or trees so they're a bit impractical as houseplants. They're probably about as easy to grow as most houseplants.
Maihuenioideae only genus, Maihuenia, which even fewer people have much experience of growing. M poeppigii is famous for tolerating cold wet conditions in winter and it's probably stretching the definition of a houseplant.
Opuntioidea a number of genera the best known being Opuntia (prickly pear), Cylindropuntia (cholla) and Austrocylindropuntia (cholla). This group is common and generally famous for their indestructibility (the main exception being the genus Puna), to the extent that some countries, such as Australia, have put legal restrictions on their cultivation for fear of them getting out of control and causing ecological problems. O. fragilis is probably the most indestructible of all cacti, with a natural distribution range that goes up to around the artic circle (this is so hardy it's rather bending the definition of a houseplant). They're very variable in size (although the hardier species are all small) so while some are unweildley, fast growing trees, some are suitable for a windowsill cactus collection (e.g. Grusonia, Tephrocactus, Pterocactus and Tunilla but there are also small species of Opuntia and Austrocylindropuntia).
Cactoideae many genera including Cereus, Echinocereus (hedgehog cactus and claret cup cactus), Echinopsis (hedgehog cactus), Gymnocalycium (chin cactus), Mammillaria, Notocactus and Schlumbergera (Christmas cactus). These vary hugely in appearance, size and cultivation requirements (this group includes plants of deserts, mountains, beaches and tropical rain forests).
Desert and mountain types Generally what you expect of cacti with fleshy, leafless, spiny stems but many are small. Most will survive at least light frost. Echinopsis are famously easy to grow. A number of genera like Lobivia and Trichocereus are now generally included in Echinopsis but they're mostly easy to grow although Trichocereus tend to grow huge. Lobivia silvestrii (A.K.A. Chameacereus silvestrii, Echinopsis chameacereus, peanut cactus) is easy to grow even for this group and could well be the most easily grown cactus that doesn't belong to the Opuntioideae. Mammillaria includes some very difficult to grow species along with some famously easy ones like: M. boccasana, M. prolifera (aptly named and surprisingly hardy for a more southerly species) and M. vetula ssp. gracilis. Some like Echinocereus triglochidatus, E. viridiflora, Escobaria missouriensis, E. vivipara and Pediocactus are so hardy that they don't really count as houseplants.
Epiphytes these grow on trees in rain forests. They tend to be less fleshy than other cacti, often with flattened, leaf like stems (no real leaves) with weak or no spines. They like similar conditions to normal houseplants and tolerate more wet, humidity and shade than most cacti. Therefore they're good if you want a cactus to grow with other houseplants, especially orchids and bromeliads. Schlumbergera buckleri' (old fashioned Christmas cactus) is probably one of the easiest to grow; this lacks the pointed teeth on the joints ("leaves"). Other easily grown ones are those with more fleshy stems: Aporocactus (rats tail cactus, now included in Disocactus), it's hybrids Aporoepiphyllum (Aporocactus x Epiphylum) and Aporophyllum (Aporocactus x Epicactus) and Pfeifera (sometimes included in Rhipsalis).
Commelinaceae only common genus Tradescantia (spider wort, wandering Jew). Some species are hardy in cold climates and don't really count as house plants. However the less hardy species are easy to grow and tollerate a range of condtions. A few are considered borderline succulents (most notably T. sillamontana) and T. navicularis is most definitely a leaf succulent.
Crassulaceae (best known genera: Crassula, Echeveria, Kalanchoe, Sedum and Sempervivum) consists mainly of small, easily grown leaf succulents. As well as the normal succulent tolerances, most will survive at least light frost, which will reduce Aloes to mush. However they are susceptible to mealy bugs, don't like systemic insecticides and tend to go into a terminal sulk if they don't get a cool winter (I won't say winter rest' because some, most notably Aeonium, grow in the winter). By cool winter' I mean temperatures between about 0 and 10c but many will survive much lower temperatures. Some are annuals, biennials or monocarpic perennials (Kalanchoe bloffeldiana, the Flaming Katie, has monocarpic tendencies and normally doesn't grow well once it's flowered). Many (e.g. pretty well all the genus Sempervivum) are so hardy that they don't count as houseplants. The best known are probably Kalanchoe blossfeldiana and Crassula ovata (Jade plant) but many others are as easy to grow as the latter and lack the monocarpic tendencies of the former. K. pumila looks like a small K. blossfeldiana covered with white powder but doesn't go into a terminal sulk once it flowers. If you can't provide a cool winter, your best bet is Kalanchoe.
Dracenaceae (Cordyline, Dracena and Sanseveria) These are mostly large, easy to grow leafy plants. The only difficult one I've come across is Cordyline terminalis but I have found that cats like nibbling the leaves of Dracena marginata.
Cordyline and Dracena are borderline succulents, which means that they tolerate drought but don't look very cactusy. C. australis is fairly hardy and will survive a few degrees of frost.
Sanseveria (snake plant, mother-in-law's tongue) are leaf succulents so they look more cactusy. They tolerate pretty well anything except frost.
Hyacinthaceae (bulbs) The two best candidates for indestructible houseplants in this family are probably Ledebouria socialis and Ornithogalum longibracteatum (pregnant onion plant). Both are bulbs that insist on growing above the soil and have similar cultural requirements to Aloes.
Lamiaceae (mostly things like mint and sage) the only houseplant genus in this family is Plectranthus. Some (the ones with colourful leaves) are monocarpic but the other species like P. verticillata and P. amboinicus (Cuban oregano) are easy house plants.
Liliaceae (used to be a large family but has been split up into Aloaceae, Hyacinthaceae etc.) Chlorophyllum comosum (spider plant) is an extreamly easy and tolerant plant.
Nolinaceae or Ruscaceae (Beaucarnea) There is only one common member, Beaucarnea recurvata (pony tail palm). This looks like a Dracena with a swollen base and eventually grows into a large pachycaule or caudiciform tree. It tolerates a wide range of lighting conditions and drought but does grow very large!
Oxalidaceae (Oxalis) O. carnosa is an exotic looking plant with tuberous roots, narly stems, clover leaves and yellow flowers. This is deceptive because it's pretty much a weed and tends to seed itself around, proving its tolerance for a wide range of conditions. Only tolerates light frost.
You probably now realize that the selection of indestructible plants is bigger than you thought. Remember you can always experiment and observe your plants. If they become elongated it's too dark, if they turn mushy at the base they're probably too wet (you'll have to cut the top off and re-root it) etc. Try to figure out what's going wrong. If you're afraid of spending your money on plants that are going to die, you can buy things from garage sales (usually a sign that they've survived neglect) or find plants that people want to get rid of. Many of these plants can be easily raised from seeds and/or cuttings. Try those Chorophyllum cuttings or Echinopsis seedlings in different rooms or composts. Once you get some easy plants growing, you may even want to try something more challenging.