I have DOS 7 (ripped from Win98se) installed on one of my drives, I installed audio drivers, properly set up EMM386 and himem.sys, etc, and everything works fine except for one thing: VESA compatibility.

For example, in Grand Theft Auto, I can run the game fine in low-color mode, but if I try to run it in high-color, it gives an error about VESA. But my knowledge on what VESA is or does is limited. As far as I know, it's a set of standards that are built into the hardware of video cards, but needs a driver to make use of it.

Anyway here's my question... Are there any universal or generic VESA drivers for use in DOS, or would I have to find a DOS driver for my specific video card?

yes there are.
try looking for univbe (from scitech)

they have a free dos version on the site somewhere.

Thank you very much.

Here's the link to the program in question for anyone else interested.
Scitech freeware