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Persian is a beautiful language when spoken.
easypersian.com was one of my main resources when I was getting started with Persian.
Persian for you is a radio course which offers basic phrases and vocabulary. Unfortunately, the links to many of the lessons seem to be broken. I have the mp3s in my hard disk, in case anybody is interested.
There is a Persian version of Deutsche Welle, which includes an audio section.
GLOSS, the Global Language Online Support System, makes a very good job at covering written and spoken Persian at all levels.
Persian in Texas is an excellent collection of resources.
Javid Jamae produced a frequency list of Persian.
If you read Russian, and even if you don't, you'll be interested in Ilya Frank's Persian texts. If you haven't heard of Nasreddin Hodja, I recommend downloading his stories. They are fun and lighthearted, yet wise and ingenious at the same time.
iranianlinguistics.org has compiled many http://www.iranianlinguistics.org/wiki/index.php?title=Persian at their wiki. Hopefully, you won't have to view the history to undo the spambot attacks.
Jon Dehdari has applied natural language processing to Persian. He has produced a dictionary and a frequency list, among other interesting resources.
On a completely random note, you can watch a short clip of Spongebob Squarepants in Persian at YouTube.
I started learning Persian the second day of 2010 using easypersian.com.
I bought a Persian dictionary from Iran which arrived to Chile three months after I ordered it.
Then I bought a phrasebook on October 2010, even though it was becoming obvious that I wouldn't be able to commit to Persian as needed in order to learn it to a good level.
I started Japanese after Persian, on November 2010.