we just transitioned our 18 month to a twin-sized mattress on the floor (in a corner of the room). actually, it's a 4 inch foam matress topper which is comfy enough for her and lower to the ground. i love it so much i wish i had done it sooner. it took a couple nights of easing her into it (she slept in a crib previously and really did like it...i think the openness & newness was a little freaky for her) but it was way easier than i thought, took maybe 10 minutes of me sitting in the rocker while she got comfortable, and i got lucky and never had to deal with her constantly getting out. even if she had, it wouldn't have been a big deal, i just keep her door closed. it's so nice to be able to come in and cuddle with her when she wakes up.
i had wanted to do it way younger, montessori-style like pp mentioned but i just kept putting it off. next kid might get one as soon as they move out of our bedroom.
i honestly now think a crib matress would be a little small. we just spent the week at SIL's house and i had her on a crib matress on the floor and she fell off so many times one night, waking up crying, that i moved her to a pack and play.