i know that the closer the rim width to tire width the better but i have set of eagle alloy 16x8 and i want to run the new bfg km2 315/75r16 on them which are essentially 35/12.5, what is the down side of running only a 8 inch wide rim with these tires? i just dont want to have to buy a new set of rims when i already have a good set  

don't worry about it... i've seen 35x12.5's on old ford 7" rims and they ran just fine... they just end up looking a bit ballonish... but i wouldn't worry  

i think you will be ok running 315s on 8 inch wheels. go gor it.  

" know that the closer the rim width to tire width the better"

That is not necessarily true. There are a lot of advantages and not so many disadvantages to running a larger tire on a smaller wheel, within reason of course.

I'd list it all out... but my brain isn't alive  yet and I don't feel like writing a novel. I'll let our other knowledgeable members here fill you in.  

I run 315's on 8" wheels, there is no problems there, It may be printed on the tire that it's recommended for a 10, If it was a 13.5 then there may be and issue. some manufactures recommend 8" wheels for their 12.5" tires like interco, It is printed on my trXus m/t's 34x12.5-16's they recommended a 8" wheel, I have them mounted on factory moab wheels.