Should I recover cabinets? And with what?

http://homeguides.sfgate.com/fix-peeling-cabinets-mobile-homes-24821.html

id paint with a water proof paint

Sand, prime, and paint. Your countertop has a problem also.

Make sure they are clean and dry. Remove the doors and hardware. Mark the doors and cabinets with tape where they go. Lightly sand the doors and cabinets to remove any gloss and roughen the surface for paint with 120- to 220-grit sandpaper. Use a tack cloth or damp rag to remove dust after sanding. Prime with a stain blocking primer like Zinsser 123, KILZ,or BIN and have it tinted to the color of the top coat. This will prevent dark or stained surfaces from showing through the top coat. Acrylic, or water-base, paints are low-fume and clean up easily with water. Alkyd, or oil-base, paints require good ventilation because the paint contains solvents that can irritate your lungs and make you feel sick. Alkyd options require mineral spirits for cleanup, but they provide a hard, durable paint finish. Whichever you use, buy the best-quality paint you can afford for a lasting kitchen cabinet finish. Seal with at least three coats with a water based polyurethane. Use a small foam roller and foam brush for a smooth finish.

First I'd find out if they're real wood or particleboard (pieces of wood glued together ). They look like particleboard or something similar and not real wood to me but I can't tell from the pictures. If they're coming apart they aren't real wood.

I agree with Tammy. If not real wood don't waste money? Save up until you can replace,you have put up with them this long. One other option is to cover them with a contact paper that is fun,not trying to mimic wood or stone finish. That way you can wipe clean. Cheaper and less work involved.

I had the same kind of cabinets. I decoupaged napkins over them. I should say torn pieces of napkins for the background, then some of the larger images over that.. Looked much better than peeling, chipping particle wood. They were easy to wipe down also.