I think the Sly Cooper series might work as a TV show, but it seems that they're pretty much done making those games, so I guess there's not much point.
A very important point raised by Anyone00 is that back then, there was plenty of room for the makers of a game-based show to come up with new characters, subplots, etc. but these days there's not really as much potential for a show to expand on the game due to games having more detailed graphics, stories and cutscenes. For example, with the Sly games I mentioned, while I do like the characters, the thing is that they have a fairly set continuity, and there's not really much room for an episodic show where they could have stand-alone half-hour adventures. Unless they were to adapt specific levels, or the stories of the three games, into episodes, but I think that would be pretty redundant and boring to watch.