You need a "remodeling" can fixture. It installs in an appropriately-sized drilled hole in the drywall. It is more difficult to retrofit into old lath&plaster however.
Special carborumdum-edged holesaws are sold in the appropriate sizes for these fixtures. The switched wire must be in the location you wish to have the light, but if you use the box that comes with the can as a junction box, you can "fish" another wire to another remodeling can and continue to add more cans this way. You may run into difficulties if and when you need the wire to go through a joist, but flexible extra-long drill bits are made just for this purpose, so it's not insurmountable.
Casey

That sounds great but my situation is a pain. I have basemeny lights and we want to replace them with cans. The existing lights are hanging off of piped in junction boxes. The first light has incoming and outgoing conduit with the hot lead running straight through it. NO PIGTAIL. So I have to cut the hot wire, disconnect the junction box and hope to move it to the side (probably won't be able to), connect all the lines to the can light with pigtails, OH MY GOD!!!!!!!!!!! PLEASE HELP!!

You realize that can lights are not going to have the spread of even "close to the ceiling light fixtures."

What Brick said.

With cans, you need several times as many fixtures for even lighting. This greatly increases the installation cost and the operating cost.

Recessed cans are just about the worst possible choice for general room or task lighting. However, when you get one of the glossy "do it this way and buy the stuff from us" magazines in the big box stores, that's what they show. So many people have no idea that anything else might be more effective or efficient.

Most likely what you have now will be cheaper to operate and more effective, almost regardless of what it is. I say save your money.

PS - I clean our light fixtures from time to time, using the brush attachment on my canister vacuum. Takes a few seconds for each. Since I have compact fluorescents in all of them, relamping is infrequent, and I use relamping as a reason to do a more thorough cleaning.