I don't think I have many plants, but my parents and friends seem to disagree.
I try to keep an up to date list, but I'm usually propagating something and waiting to see if it will take before I add it, and sometimes I just miss one. But here's my list as it was last time I checked:
With my parents (for now)
Orchids
Phal Great White NOID
Phal Sogo Yuukidan 'V3'
Phal bastianii
Phal (Doritis) pulcherrima 'Coerules'
Dtps. Rong Guan Mary
Dtps. I-Hsin Ice Coke 'KH7155'
Brassia Eternal Wind 'Hawaiian Breeze'
Howeara Puanani 'Lavaburst'
Paphiopedalum 'Macabre'
Maxillaria tenuifolia
Dendrobium nobile 'Swallow'
Dendrobium kingianum
Others
Clivia miniata (2)
Hoya spp. (carnosa, carnosa variegata, and 'Mini Bell')
Platycerium bifurcatum
Aeschynanthus radicans variety
Adiantum raddianum (not 100% sure of the species)
Pellaea rotundifolia
Schlumbergera truncata
Ceropegia woodii
Satsuma mandarin orange
Begonia masoniana
Begonia sp. (miniature angel wing type)
Sansevieria trifasciata 'Laurentii'
Billbergia nutans
Bottle Garden (5 gal)
Begonia sp. (miniature angel wing type)
Polystychum tsus-tsimense
Maranta leuconeura var. leuconeura (3)
Ludisa discolor
Fittonia nervosa
With me (again, for now. lol)
Orchids
Phal yellow NOID and green/red-lipped NOID
Phal stuartiana
Phal philippinensis (Joan X Cascade)
Phal equestris
Neofinetia falcata 'Pine'
Isabelia virginalis
Leptotes bicolor
Bl. Sunset Glory
Ludisia discolor
Others
Neoregelia 'Zoe'
Neoregelia ampullacea
Cryptanthus varieties: Black Mystic, Strawberry Flambe, pseudoscaposus, Opal, SE27, Ruby, and two NOIDS
Anthurium scherzeranum variety
Vase (Hypoestes 'Red Splash' and Selaginella kraussiana 'Brownii'
Crassula argentea 'Gollum'
Dracaena marginalis
Ficus elastica
Aloe variegata
Ceropegia woodii 'Pink'
Peperomia argyreia
Various tillandsias (about 14)
And waiting in a greenhouse until they are established in their pots:
Aechmea fasciata
Dracaeca godseffiana
I may end up with more by the end of the year. I work in a conservatory at my college and can propagate anything I want.