The equivalent of an iPod in the Android world would be one of these two:
- A handset with no telephony at all, this will be WiFi only
- An example of this is the Samsung Galaxy Player.
- A prepaid handset phone, this will still connect to WiFi, but later on if you wanted, you could connect it to a phone network
- An example of this is the LG Optimus V on Virgin Mobile.
As long as the manufacturer supports it (check the product page, but I think most do nowadays), you'll be able to download apps from the Google Play Store. You will also be able to download from alternate stores depending on the device. Finally, I think all Android devices can download from the Amazon AppStore.