No iPods have FM tuners that I know of. However, for about $50 you can buy an add-on FM tuner. I bought one and wound up never using it, so I returned it and can't speak for how well they work. But as Senusret said, the Zune does have FM radio built in. It's one of the (few) things the Zune has over the iPod, IMHO.
When I was looking at iPods & Zunes, I went with the iPod primarily on color
I had an older iPod but didn't use it much because it was such a beast, so I was kind of starting fresh. At the time, the Zune had just been released & came in ghastly colors that just didn't do it for me. So I went with a red iPod Nano and am quite happy with it. I've had an iPhone for more than 6 months and have yet to transfer a single song on it, but I'm sure I will eventually. I should note I like the Nano for pure size & portability, mine doesn't have video or anything else.
Another option is to check out refurbished iPods, sold through Apple. They fix up the insides as needed and put a new faceplate on it so you'll never know the difference. We bought 2 refurbished classic iPods for my brother-in-law & sister-in-law in Brazil as wedding presents (they're like $1000 in Brazil!) and a refurbished shuffle for each groomsmen in our wedding. It's a great way to get more with less.
ETA: If you do go the iPod route, be sure to get any case you want now instead of later. Every time they change versions, they alter the look & feel ever so slightly, which means they make new cases, which means you can't find the cases that fit yours anymore.