Just found this today, thanks to llieno. Hi-freakin'-larious, it's an online comic that has all ten of the Doctors causing havoc and saving the multiverse, one snarky quip at a time. Many different companions, many different enemies; some knowledge of the Whoverse helps, but it's a great read and seems to capture the essence of each Doctor enough that you really don't have to know much. the artist/author also has synopses of where he's pulling his references from under each comic, which helps keep casual fans up-to-date. As with most stories this wide, it helps to have a score card, but so far I'm not regretting a thing.
Currently 102 pages, still in progress. For the potentially spoiler conscious, it's 10th Doc post Rose, just after Runaway Bride. Absolutely no plans of incorporating anything after that, it's confusing enough as it is! Yes, it includes Paul McGann as the 8th. Sketchbook style, and I happen to think the art gets better as it goes. I had several moments where I literally heard the appropriate Doctor speaking lines, so that's a major plus. Read this, I think you'll like it :)