Thank you, cypherdoc. So if I were to post my wallet address A to this forum (for tips/donations/whatever), and I sent BTC from A to B they could trace the funds back to me?
Well yeah, 'they' (that is, anyone) can see that the funds in B originate from A. Transactions are public. However they can't tell if B is also your address or someone else's.
So yes, they can trace back the funds to 'you' (if they know A is yours) but they can't tell for sure if you still own the coins or if you paid them to someone else.
But there are ways around this, like coin mixing services etc.