How can I remove and replace the veneer of my bathroom vanity?

http://www.hometalk.com/search/posts?filter=repair%20veneer

combine warm water and vinegar in spray bottle, spray on, give it a five-ten minutes and scrape and peel away.

mine did that as well I just pulled off the veneer and now going to paint them

I used a hair dryer in a circular motion for like 5-10 seconds on high on each spot as I pulled. It heated up the adhesive and pulled right off in a sheet. So easy!

I would use the hair dryer option... although sometimes it just peels off in large sheets. We painted ours by priming with an oil-based primer (especially with MDF) and then painted normally... they look great and we avoided the replacement cost!