The transaction has probably been sent, but the reason you're not seeing it would probably mean that it has yet to be included in a block, and therefore can't be found through the payment information from blockexplorer.com. It also takes blockexplorer some time to update its database.
Mybitcoin listens to the network and shows bitcoins as received in the account before they are in blocks. You can locate pending transactions yourself by searching for your address here: http://bitcoincharts.com/bitcoin/
Normally it shouldn't take long for transactions to show up. If your client is online when the transaction is sent you'll often see it as "0/unconfirmed" after a few seconds (because the client listens for transactions that are broadcast over the network as well, but it may miss them sometimes), and it should be included in a block and getting confirmations soon after that – the actual time depends on the priority of the transaction and how busy the network is, but normally somewhere between 20 minutes and an hour for the average transaction.
But, there are exceptions, and sometimes you may be unlucky and have to wait a bit longer before the transaction is processed.