Can I get Bitcoins anonymously by having a friend perchase them from an exchange and tranferring them to me?
At best, you're going to get Pseudonymity doing things that way. A determined adversary will know that your friend got the bitcoins and transferred them to someone. It wouldn't take that much digging to find out who your friend transferred those bitcoins to. 

For example, if you were to purchase something illegal with those bitcoins and law enforcement cared about it, they would find out that these bitcoins at one point were with your friend. At that point, they'd go and find out from him who he sold the bitcoins to. You would be found out very quickly if they can locate your friend. This is, in fact, the sort of thing detectives do all the time.

You'd have much better luck tumbling your bitcoins.