I recently bought my first bike, a 1993 Suzuki GS500e.  I had zero issues with the bike for the first 2 weeks.  Then one day I was out riding, going about 60mph, when I feel the RPM start to jump around.  I could not accelerate at all, and the RPM's eventually dropped, and I stalled out.  After this, I couldn't get it started at all.  Had to get it towed back home.  Next day I tried starting it, and it seemed fine.  I drove it around for about 3 minutes, then oil light came on, RPM's jumped around, then it stalled out.  Had to push it back home. 

I did some research and found one person who had similar problems, and attributed it to the gas cap.  My gas cap was pretty old, and was cracked a little bit, so i replaced it.  Unfortunately, this was not the fix.  I then decided to change the oil, since I wasn't sure when the last time it was changed.  I fully drained the oil, which was almost black. Then put a new oil filter in, and the new oil.  Started her up, and it seems to idle better, and was a bit smoother with RPM's.  Until it sputtered, and stalled out again. 

I'm now thinking the carbs could be gummed up, so I bought some Seafoam and I'm going to see if that makes it any better.

Does anyone else have any suggestions or ideas?

You making no oil pressure your oil light still coming on ?
That is a very serious issue. Fix it first before anything else.
Cool.
Buddha.

Why are so many people reactive and not proactive?
Rode the bike 2 weeks and didn't know when last oil change was on an old bike? 
Some people deserve their problems. 

So the oil light comes on when the bike is still running?

If you can run the bike without the light coming on then checking the oil pressure is probably a good place to start

I'm reactive because I don't know much about working on motorcycles at the moment.

Yes the oil light comes on when the bike is running in 1st or 2nd gear for a few minutes.  If i leave it in neutral, the light does not come on at all. 

Yeah like Buddha says that could be a serious problem. The light isn't for oil level it's for oil pressure.. big difference. I wouldn't push your luck... no oil pressure could equal dead engine, if there's no oil being circulated it's going to chew your cams and anything else that wants to go with it.

Haven't dealt with this myself but there are plenty of threads on gstwins just Google gs500 oil light and start reading. Could be a bad sensor but first thing you need to do is find out if you have oil pressure... either connect a oil pressure tester or ghetto test it by pulling plugs and cranking (it'll get messy) see Bob Broussard's post about that. Good luck.

Yeah I would do a oil pressure test first, there are instructions in the service manual on how to do this

sounds like it could be the fuel starvation issue too. check the petcock. put it in prime and test

I drained the fuel from the tank, and put in some fresh fuel.  Put some Seafoam in for good measure.  Ran around for about 10 minutes just fine.  Going to take it out for a bit longer today, so hopefully this ended up being an easy fix.

I don't think the previous owner had filled up the tank with new fuel in awhile. 

Does the oil light come on when you turn the key - before you hit the start button
If not, that light is blown out.
That light has to come on when you turn the key to on. And never come on 1 second past start up. If its sat a while, or you did an oil change - then it can stay on for 3 seconds.

Cool.
Buddha.

Oil light goes away right after i press start button.  Ran it for about 20 minutes yesterday, with fresher fuel, and seems to be good. Hopefully...

Can bad fuel really cause the oil light to come on? How long before fuel becomes "bad"?

Low oil pressure can cause oil light to come on! .... add more oil to correct level or change your oil! (And filter).

Depends on the load of fuel, how much moisture was or is present when you got the fuel, how long it sat in the tanks at the fuel station, how clean their tanks are etc etc. ..
It has been said by the Yankees that 'about a month or so, especially with e10 fuel!' ... I've sat mine for months with no big effects but I'm really picky about where I buy it... and I've used e10 on purpose for the last 18 months. .. had to replace stiffened fuel lines. . But whether stiff due to e10 use or age? .. don't know...

In the end. .. fresh clean fuel is ALWAYS better!