Notice: If you want a payment to go through in less than several hours, increase your Bitcoin client's optional/voluntary fee to something higher than 0.0001/kB for all transactions. Priority is given to higher fee transactions.

Some transactions sending large amounts of Bitcoin may qualify to be free, but you should add this additional fee in your Bitcoin's options, so that no transactions are sent without fee. The default additional fee is 0, which still allows some non-fee transactions to be created.

The Bitcoin network is very busy right now. There are several transactions a second being sent, and currently 6000 and 5MB of transactions are waiting for inclusion in the blockchain. Inclusion is what makes payments confirmed and trustable. If there were NO more transactions sent, clearing this backlog would take over an hour of maximum-size blocks.

Just the web page attempting to list unconfirmed transactions is about 2MB, and will make your browser crawl:
https://blockchain.info/unconfirmed-transactions


Also note: If you have already sent a payment with Bitcoin-Qt, the best thing to do is wait. Other wallets may make "bad" transactions, with less than the mandated minimum fee that will never confirm, but Bitcoin-Qt transactions will always confirm given time.

The first-post instructions for removing a transaction and re-sending a new one with fees apply only if the original transaction was created with a "bad" client, or if it was sent while attempting to bypass Bitcoin fee rules. Removing a transaction record from your client and re-sending another transaction will likely do you little good. The network won't soon "forget" your original transaction if it is properly constructed, will recognize a new transaction as attempting to double-spend the same money, and will discard the new transaction anyway.