Why does my televison have no power?

I have had two televisions just quit working in the last two months. They are older models, but have been working fine. One was a 26" Zenith that is about 10 years old and quit working about 2 months ago, and the other is a 32" RCA about 12 years old that just stopped yesterday. They were working fine, and then when we turned them on one day they just didn't work. It just seems odd to me that they work fine one day, and then the next day they are just dead.

Any suggestions would be helpful.