Apex AD-1500 DVD Player
Pretty good bang for your buck.
I haven't had any major problems with the AD-1500.  The remote is slick and does everything you need while watching a disc.  But the remote doesn't turn the power on/off; you need to push the big button on the unit.  Discs have skipped a few times but who knows if that's the disc or the player.  I don't really use it much to play mp3's but it seemed to function well enough doing that, but you can't FFWD or REV songs, if I recall correctly.  So, you don't need to go with a big brand name just for the prestige.  I think an Apex will do for most, especially poor college students like me.