First off - ignore all those idiots hawking Limewire (or its half-sib, Frostwire). These are peer-share clients - programs that hook you up to a network of other users who share media. Peer-share (or p2p) is not inherently problematic, and they are theoretically a great way to get pirated media. The problem is that the popularity of some programs (esp. limwire) has some negative effects - it attracts n00bs and leeches who expand the user base w/o bringing files; it also attracts hackers who offer malware-infested files on the internet.
Alternative p2p - get winmx. Rumored defunct as of 2005, it's still going strong, with many new audio and video files, and poses little threat of malware. Another great program is eMule (be careful - there are hacked versions of eMule on the internet; googe "eMule" & "malware" and you'll get the idea.
You can simply record music streaming from the internet, whether from sites like youtube or online radio stations. Programs like audacity will record streaming audio and even edit those recorded streams if you find one song you like out of an hour-long stream.
CD's - remember them? Easiest way to get music, since CD's are still easy to find for free (friends, relatives, the library) and as easy to rip (realplayer or wimp).
Many unsigned bands maintain websites where they offer some of their stuff for download.
"Without using itunes or an ipod?"
Why do you think you'd need an iPod or iTunes to get your music from the internet? It's other way around.