whats is the widest rear tire you can put on a 1980 camaro with out making any modifications?

 

these opinions are based on personal experience and web confirmations do so at your own risk always measure your wheels fresh out of box to make sure they are the correct sizes and on the axles before mounting your tires.
stock 15X7 iwouldn't go more than p255-60 rear and 245 in front, 245 all around on 15x8's are cool if you put spacers on the rear to your preference. although iput a p285-70 plus series truck tire on a15x7 wheel on a 1972 buick skylark once in 1993 its wheel wells have more room to start with than a camaro.
1.So this really depends on wheel size here I shall cover 15" wheels as ihave little experience with larger wheels and know that the right size can fit larger tire from the start just too thin and traction limited for my tastes, for me the side wall is what helps it grab and scoot. 2.Also and what you consider 'mods' to be. some camaros have rearends shifted left or right of exact center so results always vary . no major mods but you can beat the seat belt humps in the rear wheel well with the tire off with a big rubber mallot, or block of wood and any hammer to flatten they move right in easily for me.
try a set of p275-60 R15 on a 15X10 and 5.25" BS (backspacing) or P295-50 R15 most wheels come off the shelf with 5" or 5.5" bs so you will need the 5.5" BS with a 1/4" spacer and recommend the correct aftermarket wheel studs with correct lug nuts for the wheels , I personally like weld wheels, centerline, or cragars. on a stock 15x7 or 15x8 -4.5" BS I would go P275-60 R15 maximum. those are likely to rub though. 15"X8" with 4.5" BS for the p275/60R15 are ok but the 15x10 with 5.5"BS and 0.250" (1/4") spacer fits better with the p275-60R15 .
If you do not use the p295 but go with the p275 on a 15" wheel you may get away with 5" BS. There have been some rubbing issues with these tires in some cars or on big bumps and on fender edges that stick in , those bend up also but this may require more body work. Always , Always measure without the wheel and tire on and with the wheel on before you install the tires in case you need a correction and need to send the wheel back or for another wheel. keep checking what everyone else is saying also. In my opinion ifeel if you got an aftermarket 15"X10" wheel with 5.5" BackSpacing or 5" B S and 15X10 or 15X9 , the P275-60 R15 is pretty good and basic. use some modern low profile traction bars and performance shocks. important to note the diameter height of these tires the 295 is around 26.8" or 27" and the 275/60 is slightly taller 27.5 to 28.5" or 28", depending on your gearing you may need a speedometer gear change its real easy its the mechanical gear on the speedometer drive cable that plugs into the transmission they are removable and interchangeable with gm style speedo gears for auto or manual transmissions, they are usually readily available last ineeded one , but whom knows what has happened with that the last 10 years. the tires iam talking about are the bfg radials you might try the Goodyear eagle modern sport tires also.