Cloth diapering isn't just for people in houses with washers and dryers. It seems like it would be a pain in the but the wash cloth diapers if you live in an apartment, but you actually have a lot of options of how you can do things.
The apartment that I am moving into has NO W/D hookups and NO on-site laundry facility. It's a 4-plex (one building, 4 apartments) and it's a fairly old building (I do however have a sort of yard, and I saw a hammock hanging between two trees). The laundry situation isn't ideal, but it made me do some research. Upon searching I discovered that yes, there is such a thing as a portable washing machine, and no, you don't need hook ups for it. If you have a kitchen sink then you're good to go. They even make some small enough to fit on your counter top! I'm planning on hopefully getting one before I move (if I can save up/sell enough stuff), I am choosing one that has a 12 lb. capacity (since dirty diapers are pretty heavy) and it's approximately $229. If you think about it, if you are an apartment dweller in a similar situation you could get one of these washers and an entire stash of cloth diapers and still save thousands of dollars. Once you spend that initial money then you're done spending money on diapers entirely.
I figure that since I live in Texas and it's going to be hot/warm until Halloween, that I can air dry while I save up for a portable dryer.
I am going to try to update more often, and I especially want to update my cloth diapering journey going from a house with a washer and dryer out back, to an apartment with none of the above.