The current block count can be seen here:
 - http://blockexplorer.com/q/getblockcount

To learn how to use that number for verifying that you are current, see:
 - http://en.bitcoin.it/wiki/Getting_started#Initialization

You might want to make sure you are using the latest client.  It includes improvements on how blocks are received:
  Help -> About
You will then see the version number.
The latest is v0.3.24 (Bitcoin version 0.3.24-beta).

If you are current on all the blocks but still have a transaction that is not confirming, then make sure to leave your client running so that the transaction can be resent.  Some small transactions and others where no transaction fee was paid may get considered "very low priority" transactions and as a result can stay unconfirmed for a while.  To see if it is getting announced to the network, see if it shows up in:
  http://www.bitcoincharts.com/bitcoin
If it does show there, then patience is needed.