[zaphar]

    For example, you take your ill-gotten gains and just randomly send $1 to a 
    million different addresses, some owned by you, some owned by random people or 
    exchanges or whatever. Nobody's going to say no to free money, so the trail 
    goes cold.

This one wouldn't really cause the trail to go cold though. It would be trivial to automate the tracking and if all of those funds end up in a single location eventually that would also be trivial to automate tracking. You really would need to do a Mixing with other counterparties to get any kind of anonymity. Even then mixing can be detangled as well.