I can only speak from my own experience, but my experience has been thus:

I have a machine that runs Windows 98 Second Edition (you should try to get SE if you can because its more stable), and it has been able to play every game I have thrown at it.

Now, you may have to do some tweaking--I personally configured mine to have a boot menu, and I had at least one Windows 3.X game (Outpost) which, in its original release, required you to tweak some windows files so the install would work. But its not hard to do.

Also, I recently discovered that some games can have weird issues that don't seem to be related to the Operating System. For example, some Sierra adventure adventure games (on my setup) only had sound if I claimed my soundcard was a Thunderboard (its really a Soundblaster 16)... and then, doing that caused them to start locking up if I used a ps/2 mouse instead of an old serial mouse. The only cure I've found for this is either to use an older mouse (which I don't wanna do) or use Dosbox.

I'm not gonna lie: Even if you have an old comp, Dosbox may turn out to be an indispensible tool, so keep a copy around regardless.

But, long story short:

Windows 98 SE will run any DOS, Win 3.x, or Win95 game you throw at it. Sometimes with a little effort, but they WILL run.