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You can trace all transactions forever, they're all public in the Bitcoin ledger (blockchain). But since Bitcoins are fungible, if you transfer them to an address that holds BTC from many people, you can "mix" them and make it harder to tell to where did your amount go: https://en.bitcoin.it/wiki/Mixing_service

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You can also use alt-coin exchanges, e.g. BTC->LTC->BTC, or even multiple exchanges (one to buy, one to sell) to obscure the trail even more.

Keep in mind older transactions are pruned from the tree on most nodes. While you may see where a Bitcoin originated, not all intermediate addresses will be shown forever in some version of the Blockchain. That's not to say that someone somewhere doesn't have the full blockchain, so you should keep in mind that it depends on what blockchain you are viewing at the time of investigation.

If I were the NSA, I'd be keeping track of the full blockchain.

Based on current observations, I would assume they are and have for some time.

That's not exactly true. Older transactions aren't indexed by most nodes, so it's a lot of work to retrieve them, but almost all nodes still have a full copy of the entire transaction history.

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