Most of the major brands are quite reliable. I have always had excellent experiences with Panasonic. The only Panasonic product I ever had a bit of trouble with was a microwave that was repaired under warranty and hasn't exhibited any problems since. Panasonic is consistently the top performer in the Consumer Reports reliability charts followed closely by Pioneer.
I work in the industry and while the business I work for represents a tiny sample I can certainly say there are some trends as far as brand reliability goes. The store I work for is also a service station for most major brands and we handle service work for many extended warranty companies, Best Buy, Circuit City, Frys, and others.
Samsung is a brand I thought very highly of before I had my current job. While Samsung LCDs are better than their plasmas they definitely have a higher defect rate than most other brands. The other thing about Samsung is that there support is not very good and they are frustrating to deal with from a service center perspective. I have lost quite a bit of enthusiasm for Samsung. I would never buy a Plasma from them after seeing the number of problems they exhibit. I don't know if we've sold even one in the past 2.5 years that hasn't needed service within the first year. That's not good. Their LCDs aren't as bad but quite a few of them have needed service as well.
Sony is, overall, quite reliable. I have seen a few defective sets but the defect rate isn't bad.
Pioneer is virtually perfect. I can remember two Pioneer sets that have needed service in the 2.5 years I've been on the job.
Panasonic is even better. I can only recall one Panasonic flat panel requiring service.
Mitsubishi is a set I would not buy myself unless I was getting a good extended warranty to go with it. Their DLP sets have a very high defect rate within the first year. I can't count the number of Mits DLPs that have been in service multiple times in one year and beyond. Their LCD sets have had issues as well, mainly with defective panels which are produced by who? Samsung.
If you're looking for a good 32" set then I would look into the Panasonic TC-32LX85.