How do I withdraw bitcoins from my MtGox account? I've purchased a few bitcoins on MtGox. Now I'd like to spend them. How can I actually spend the coins I purchased on MtGox?

I've looked around mtgox.com for any indication of private keys, bitcoins addresses, hashes etc but didn't see anything. I'm fairly new to Bitcoin so there's probably something fundamental I don't quite understand yet.

Cheers!
Easy: you transfer them to other addresses. Go to Mt Gox, log in, select "Funding Options," select "Withdraw," select "Bitcoin" in the drop down box. You then can put in an amount, and an address of where you want to send your BC (bitcoins).

If you want to know where to spend them, check out https://www.bitcoinstore.com/ as an example. Personally, I am keeping mine as an investment - I have owned them for around 6 months and have made 150% returns. But you can also use them to pay friends around the world without paying a middleman. 

Enjoy your cryptocurrency!