How much silicon is required for the most common ICs?
Parts that are available as bare die, this information should be in the datasheet. 

Some older parts included this information even if they weren't generally available as bare die, since it might be useful for estimating reliability of the part. 

For example, here's the AD621 (actually an in-amp, not an op-amp, but it was the first PN I thought of):



So, that one is about 9.1 mm2. (I dunno how they screwed up the inch measurements so badly).