Drill a hole in the bottom of each drawer track at the front. Drill a similar hole in each drawer side at the back. Insert one of these glide buttons in each hole (four per drawer).
That should cut the friction.
You may have to modify the thickness of the button a little or the drawer front will not align as before.
Casey

Here is a link that might be useful: Nylon button

Thanks! That is a good point about the swollen/warped wood. The drawers are fairly hard to slide the whole way out. Let me clarify what each drawer look like. It is just a box that rests on two flat pieces of wood on the bottom. They don't run in grooves on the side, and there's no center runner. The drawer fits quite snugly in the slot. I think the "runners" might be structural to the cabinets, and I am not sure it would change anything to replace them. Maybe sanding to reduce the size of the drawer slightly, followed by "greasing," would help?

And no, the runners aren't painted, nor are the sides of the drawers. I think the paint is just coming from the top edges of the drawers where it rubs against the front opening as it opens and closes.

Those buttons look promising. I do think it would be a tight squeeze--maybe could sand down the drawer a bit as well as modifying the thickness of the button.

Before you go for a time consuming solution, you should give the bar of soap a try. It really works.

Or try a spray silicone, seals and glides all in one.

A candle stub works as well as the soap, if you don't use bar soaps. I have several old dressers that are constructed much like your cabinets and before rubbing with a candle they squeaked and screeched and stuck when opened and closed.

Do try the candle wax/soap. Rub it on both surfaces. You may need to redo from time to time. This has been
SOP for old wooden drawers for as long as I can remember. In fact, "soaping ones drawers" used to be the source of many giggles.

Candle wax is good; soap is less good- it's hygroscopic (attracts water to itself) so it could exacerbate swelling.

Thank you all! I will try candle wax tonight and see how it goes.

Here's another question about the cabinets. The shelves inside are very banged up, especially the edge where pots and pans bump into it. Paint chips and bits of wood come off on a daily basis. I want to work on fixing that, but I am concerned that re-painting, even if I do a good job of sanding and prepping, will not last very long and I'll just have the same problem within a few months. The wood is fairly soft (maybe pine). Can you think of something else I can cover those edges with? Something more durable than contact paper? It doesn't have to be beautiful since it's just inside the cabinets.

I repainted our cabinets inside and out. Then covered with 3 coats of Minwax Polycrilic, one coat every hour. Waited 2 days till the poly sets real hard and now I slide dishes and pans in all the time and the paint never mars. The poly can be renewed at any time and will not show marks between the coats.

My SIL is a siding contractor and when he walked in the door and looked at the cabinets he said "Wow, new cabinets?". That said it all for me.

Great suggestion, hendricus. Thanks very much!