I had the same problem with some brands of CD-R's and some players. Disks made by CMC Mag. (Imation and other names) would do what you said in a portable player or boom box but be OK in the computer or stand-alone disk player.
The only other brand I tried so far is Sony (made by Sony) and it worked well in everything.
If you use Nero, it can tell you who made the Disks.
I updated my Lite-On drive with the latest firmware and Win98(2nd ed.) with the latest ASPI driver layer but this did not change anything.
I think that it has something to do with the laser not being powerful enough in these players in order to read some disks properly.