My car has rips in the leather seats. I don’t want to spend the money to totally reupholster the seats, and I’ve read that those leather patch kits don’t work very well.
So what about just using duct tape? My seats are tan, and I can buy a roll of tan colored duct tape to seal up the rip. Does anyone know if duct tape will hold a rip on a car seat?
No.
It will probably work just fine until someone sits in the seat. 
Seriously, you might get it to hold if you extend beyond the tear for a significant distance – 6, 10, 12 inches maybe – but it will still eventually get pulled away from its original position. And of course will leave a sticky residue and look like crap.
If they are clean tears, why not stitch them up?
No.
If you can’t spring to get them reupholstered your best bet is to duct-tape and then put some cheap seat-covers over it. Duct tape isn’t going to hold forever, and it will peel up the edges, get sticky, etc. So the cheap seat covers are to protect the duct tape, and the seat of your clothes, but you’ll have to replace it periodically anyway.
No. The heat will soften the glue and the tear will pull apart when someone sits on it. Plus, the duct tape will deteriorate over time.
You can get seat covers fairly cheap.