How wide can you safely go on a stock rim? Current OEM tire is 130/90/16.

 

It's really about the distance between the tire and belt/chain. That being said,I've seen 150/80-16 used.

 

I have used a 140/90 or MU in my 1990 FLHS and currently have a 150/80, but only by using a later narrow belt. It is very close to my fender!

So as Steve says, the main limit is clearance between belt and tyre, with fender clearance second. My 140 just touched the rubber curtain on my belt guard, so I removed the curtain. I have heard of some HDF members who got their 140 in with enough clearance.

Tyre brand will have some affect, as the actual width of a tyre can differ from its nominal size. For example my 140/90 Avon Venom measured 139mm wide fitted and inflated, but my 150/80 Venom is 153mm wide.

 

Found this chart back when I was wheel shopping. Pretty good reference.

http://www.hdwheels.com/Product.htm