iPods can play mp3s files just fine. Songs purchased from the Apple iTunes Music Store uses a proprietary format called protected AAC because standard .mp3 and .aac files do not have DRM (digital rights management) technology to protect against piracy. Currently, iPods are the only mp3 players that can play protected AAC files (since that format was developed by Apple). Most other mp3 players on the market use a different proprietary format developed by Microsoft, which since Apple didn't license from them, iPods can't use. But this is all if you intend to buy music from an online music service.
Regardless, if you own CDs and rip them to mp3, then they will play on an iPod just fine, as they would on any other mp3 player.