How important is the fee for speed of confirmation? I am developing a Bitcoin application, so I am sending a lot of "toy" transactions for testing, with 0 fees.

But it seems that those take forever to get confirmed. (Right now I am waiting 45 minutes for one transaction to get confirmed. Previously it was about 30 minutes.)

Is my suspicion right, or am I doing something wrong? How important is the fee for miners? Do they preferentiate? 

Or am I doing something wrong (not broadcasting to enough nodes, maybe?)?

And do nodes, that aren't miners (with official client I presume), preferentiate to send around transactions with fees?

(edit: note that the question was written in 2012, when the blocks were still empty.)
It seems like there is some policy against free transactions in official client.

There are some anti-spam protections, which my toy transactions exactly meet (low transactions, recently accepted coins, etc)

https://bitcointalk.org/index.php?topic=63553.0

https://en.bitcoin.it/wiki/Free_transaction_relay_policy