Oh sure, the two don't line up perfectly. I can't say "D&D is like the Ramones, and Traveler is like Minor Threat, and this game is like Operation Ivy, and so forth." But it's surprising how many broad similarities there are.
We have two things that grew out of marginal movements (RPGs grew out of wargaming and pulp literature, punk rock grew out of the shunned-by-the-mainstream "proto-punk" groups of the 60s and early 70s), both of which were spread largely by word of mouth and an active, zine-based fan community. We have an explosion of national interest beginning around the same time (the late 70s). We have a slight retrenchment and expansion in the 80s (punk rock moved into the suburbs and became hardcore; RPGs moved out of the suburbs into...other suburbs...and became increasingly more complex--"hardcore," if you will). The 90s saw another mini-fad (with third wave ska and bands like Green Day, Rancid, and The Offspring for punk, and for RPGs the second edition of AD&D and games like the White Wolf line and its many, many imitators) that was sparked by a combination of old school revival and new interpretations on old ideas, while the last ten years have seen an increasing emphasis on "marketability" over being true to the scene's roots for both (the "fashion punks" like Avril Lavigne and Ashley Simpson 2.0, or the pop punks of Good Charlotte, et al., for punk and, for RPGs, things like "lite" rulesets, hard-cover, full-cover game books, and D&D 4e), along with movements labeled "indie" in both camps that focus on bringing "heart" back to their respective endeavors while expanding the accepted forms into previously untested waters, all the while traipsing dangerously close to obnoxious pretentiousness.
Now, like I said, these aren't perfect analogies--is 4e as vapid and commercial as your Avrils or Charlottes? Probably not (although the way some people go on about it...). But there is an intriguing similarity going on there, I think. Perhaps it has to do with the life cycle of any creative endeavor that engenders a "scene," be it music or collective storytelling. Or maybe I'm full of it.