I use a supermarket's own brand cat litter (which is super cheap, does what it is supposed to, and Mittens is fussy and doesn't throw this one onto the floor). I scoop it into a little plastic bag and throw it into the trash.
I remove feces from my cat's litter box once a day (twice a day, if I'm home all day).
I have a litter scooper, but I don't use it because I don't like having a filthy thing like that hanging on the wall, and I'm not about to disinfect it every time I use it.
Instead, I put my hand inside a grocery produce bag (make sure it's airtight...no holes), pick up the feces, turn the bag inside out thus encasing the feces, tie the bag in a knot and throw it away.
This is sanitary, because you never touch the feces, but due to the "yuck" factor I wash my hands afterwards anyway.
One more tip about the "yuck" factor with litter boxes: Before you put in fresh litter, encase your litter box in a sturdy, large plastic bag, secure it with clips at the corners, and lay down a few sheets of newspaper, then add the litter. When it's time to change the litter, just pull up the bag carefully, tie it up and throw it away. I dislike cleaning the litter box, and this method eliminates the need to do it.
After much experimenting, we now use a 100% corn-based litter (which can be flushed or scattered outside if you have space on your property) AND a couple of large empty boxes and one large white porcelain bowl with only a few sheets of standard TP in them. We have one cat that had to have big-time surgery for recurring crystals and do not want clumping litter. Silica was interesting, but we don't know much about it or who makes it in China.
The corn litter clumps naturally on the SURFACE of the litter, so you need to keep the box fairly full. We tried plain cracked corn (very cheap at a local feed mill), but the cats ate it instead.
As we have to haul our own trash, these methods cut down on disposal costs as well.