I'm hoping to listen to podcasts of a variety of different games, to get some idea of what's out there to be played--but a lot of the ones I seem to find (such as The Rolemonkeys) seem to be out of date and no longer run. Where are some actual play RPG podcasts still in production?
The Walking Eye is a mix of discussion and AP, but I believe AP is the heart of the show. The Gamemaster Show (sorry, I'm still limited to one link per post but it's easy to Google) seem to be having some hiccoughs, but they're rooted in AP shows too.
But my favourite, hands down, is Actual People, Actual Play, mentioned above.
For a good selection of different RPGs and systems, I suggest giving Role Playing Public Radio a try. I know they've got a good amount of different games they tend to do that are on the site. D&D 4e, Call of Cthulu, Monsters and Other Childish Things, World of Darkness, Mutants & Masterminds, and a few others I can't think of at the moment.
I'd like to advertise for Nerd Poker. Brian Posehn & his friends are absolutely hilarious, playing a mishmash of 2e and 4e, and Sark's storytelling and descriptions are stellar. It's a fun and entertaining romp that's had me hooked since the beginning.
The Podgecast is one i really enjoy. Great mix of fun! and useful rpg stuff. They're mostly on pretty solid release schedule, so there's always new episodes. The show is a bit heavy on the burning wheel side (which i really don't mind), but they cover all kinds of useful things aside from that.
another new one i really enjoy are the Jennisodes hosted by Jenn Wong. The show is mostly revolving around indie-side of RPG's. Jenn is a very enthusiastic host and the interviews on the show are fun, easy going yet informative. Also a she's got a pretty solid release schedule.
Also, take a look at this article: Bi-Annual Podcast Roundup, in which MJ Harnish writes about his current selection of RPG podcasts. Which ones have faded, which ones have caught his interest. you might find something you like there.
There's actually lots on archive.org. Sometimes you find parts out of order but you can generally click on the artist/composer to find the rest.
For actual play sessions on varied systems (specifically non-D&D), you have:
There's an incredible wealth of RPG Actual Play podcasts available at http://www.rpgmp3.com/.
Pretty much every game setting and system is represented, from mainstays like Pathfinder and the various incarnations of D&D, Savage Worlds etc., to old-school games and indie newcomers.
They've got a HUGE back catalogue of recordings, contributed from several different gaming groups from all over the world, and multiple groups are still going strong.
I would like to recommend Brian Posehn's Nerd Poker on the Earwolf network as well. He has a great group and they are all very funny. They have been playing together for years. Critical Hit from the Major Spoilers Podcast is great too. Dan Harmon also has a podcast called Harmon Town. They usually play DnD at the end of the episode and they have some great conversations on there.
One that I listen to regularly is Beer and Battle, found via iTunes. Can't recommend it over any others specifically (I never knew there were so many!), but they have a decent site that explains their setup, including projecting the maps down onto a tabletop, which is pretty slick.