What if you aren't sending from a personal wallet (Bitcoin-QT, etc), rather from an exchange (Cryptsy, mint, etc)? In that situation would it still be possible to trace where it was sent from? Or, since it is the exchange's server sending the transaction, would it be anonymous?
Network snooping will show the transaction coming from the exchange.
The exchange, of course, knows it was your transaction and they'll have records showing such.
The same people who engage in widespread network snooping probably can just ask the exchange to give them those records (or they'll hack into the exchange and just extract the records themselves).
That's why I said if you use a web wallet you don't have any privacy.
A full peer who is not masking their activity is susceptible to transaction counting. That is, detection of transactions which originated at the peer rather than those being relayed. Or at least that was supposed several years ago. Several years ago most people thought it impractical though I personally always considered it a potential threat. Now (post-Snowden) it seems likely that fine-grained packet are captured, retained, and analyzed. At least for anyone who is tagged for enhanced monitoring, and I think that there is a strong possibility that all Bitcoin users are.
A non-compromised https connection to a non-compromised exchange or wallet service (if there is such a thing) would be theoretically more safe. It would require timing analysis to match user activity with transactions (if they even leave the service) and that would be very easily thwarted by introducing some random delays. This assumes that the service is somewhat popular (and thus, active) of course.
Go ahead and say the magic words 'tor'. For my part I never trusted it. At least not for highly critical work. It being largely funded by the government to 'help Iranian dissidents' doesn't pass the smell test for me. But to each his own.
