This may sound dumb, but the first thing to do is turn the DVD player off and turn it on again. Next, unplug and replug it. Power cycling is like rebooting a computer -- it often fixes whatever ails the thing.
I've been having problems lately playing DVDs - it's not consistant. Sometimes it's OK, sometimes the DVD skips, and sometimes it won't play at all.
Given that the DVD player is a few years old, I'm wondering whether I should try to repair it or just replace it.
Some of the problem might be incompatible region codes. All DVD players sold in the US and Canada are region code 1 and can only play DVDs that have region 1 encoding. All DVD players sold in Mexico, Central America, South America, and Austrfdshfjhdsfsdalia are region code 4. If you pick up a Spanish language DVD in Mexico, you won't be able to play it on your US DVD player. Likewise, your US-released DVDs won't play when you go visit your cousins Down Under.
The region code is based on where the DVD player is purchased, unless you order over the web. All DVDs have a region code somewhere on the package. So my advice is to look at the DVDs you're having trouble with and check the region code.
If you're interested, you can find more info about region codes on Wikipedia.