IIRC the 200/1.8 had the highest performance recorded at one point, and that was when proper optical instruments were used - not camera bodies with AA filters.
www.photozone.de (Canon EOS Reviews do a great job of characterizing sharpness) ... but, picking a lens based on just sharpness and not application is just plain ... well ... silly. Learn a little about post processing and you shoudl be able to get nice results from a broad range of lenses. I just sent my mother a beautifully processed and printed image from my Canon G9 (yes a P&S!) today for Mother's day. Selected it over some other images from my 70-200 f/4 IS L, which is one of Canon's sharpest L's, based on composition and mood. Sent it along with three other prints from my 17-55mm f/2.8 IS, 85mm f/1.8 and 50mm f/1.4 ... all nice and sharp lenses.
The answers you get here will be all over the spectrum.
35L, 135L, 85L.
The 70-200 "which is sharpest" is bologna to me. I've seen samples from all 4. I've seen soft and sharp copies of each lens. I think some of the "soft" copies are user error, or quite possibly, too high of an expectation.
As for which Canon lens is the sharpest, I cannot answer. I would motion to say it's a Canon prime. From what I've read, primes are typically sharper (I almost say "optically superior") to zooms. This is evidenced in my own "research".
Quite simply, my 50 1.8 at 5.6 is sharper than my 17-85IS at 50mm at 5.6.
No matter which lens you end up with, send it in to the Canon tech guys in Sweden for calibration and it will come back better. Having said that, the 300/2.8 IS is a stunner right out of the box. I picked mine up about a month ago but I will still send it in for calibration.
The sharpest lens I've owned under $1k is the 135mm f/2L, and the sharpest over $1k is the 85mm f/1.2L. I can't speak for some of those big guns out there like the 200mm f/1.8L since I haven't used them.