I don't know whether I'd say I'm a grammar geek but I do enjoy the topic, even if my writing doesn't always represent GAGC (generally accepted grammatical constructions).
But I do enjoy reading books like Lynn Truss' (or is it Truss's?) Eats, Shoots & Leaves and I'm never without a copy of Strunk & White close by.
So I have no hesitation in recommending a podcast about grammar.
It's called Grammar Girl - Quick and Dirty Tips for Better Writing, and it's a great way to stay sharp. It's a regular 5-minute show that looks at a particular grammar issue in detail. You can find it on Itunes or you can go to the website, where you can listen, download it and also order a copy of her book.
I thought of it today because I found out through Twitter (via Donna Papacosta, host of the Trafcom News Podcast) that Grammar Girl (aka Mignon Fogarty) is featured in a video that's up on YouTube. I've linked to the video below, so you can watch it yourself. And I recommend that you sign up for Grammar Girl. It won't hurt, and you might find it helps your writing too.