Pretty much any mp3 player will work. If you're not going with iPod and iPod specific accessories, most of the time you'll be hooking the player to speakers via an auxilliary cable - one end goes into the headphone port, the other goes into aux input port (looks like a headphone port). You can connect to your car in a similar way, if it has such a port (newer cars will more than likely have one). If you have a tape deck in your car, there is an adapter for that - it looks like a cassette tape.
If you have neither (like I do), the least costly(possibly) or disruptive but most frustrating way to go is with an fm transmitter. Why I say frustrating is because they are hit or miss. What works well for one person may not work well for another. How well one works could depend on factors such where you live, how strong the stations are, and where the antenna is on your car. I tried about 6 or 7 different ones before finding one that I liked, which ended up being one of the more expensive ones. I ended up paying $90 for mine, and it is iPod-specific, although you can use non-iPods for it.
You didn't include anymore specifics, such as budget and capacity, so I'll just name a few (I'm only including lower-capacity flash-drive based players):
From SanDisk: Sansa Express, Clip, e200 Series
From Creative: Zen Stone or Zen Stone Plus, Zen, Zen V and V Plus
From Apple: iPod Shuffle, iPod Nano
You can also look at CNET's mp3 player page:
I may be an odd ball, but I want an MP3 player strictly for downloading and listening to radio programs on the web. I've taped radio programs for years using a tape recorder. I'm in the computer age now so need new equipment - just wish I could figure it out!! I need one that can be hooked up to a small speaker so I can listen to it in the garden. I would also like to listen to it in the car; are there adapters for that as well?