[paraboul]

You always give a transaction you received before in order to spend coins. However, you're supposed to use a fresh (source) address for every new transaction (the wallet software does it for you). You can't (with the default wallet software) chose which transaction (called unspent transaction) you use in order to spend you coin (this is called coin control).

That is, you can trace coins, not owners, unless you're always using the same source address.

[rayiner]

If you say, get paid in Bitcoin, one transaction a month, and that's the only way you earn Bitcoin. Will you use the same source address all month?

[judk]

The payer uses a source address, which changes because each transaction should "kill" the original source, sending it's money to two addresses: the payee and the "change" that goes back to the payer but using a newly invented address.

You can invent a new destination address each time you transact (to get paid or to receive change). You make a new address by picking a random number and doing some math.