Like someone mentioned, if someone like Coinbase has a policy of investigating the origin of the Bitcoins you send and they find out they come from criminal activities then you are in trouble, even if you had NO IDEA that those coins were in Silk Road sometime ago. This really sucks and will hinder mainstream adoption. It kills fungibility. The average end user should not care about it and not have that worry on their mind. I myself avoid stuff like Coinbase because who the hell knows where the Bitcoins that you got come from? It's a joke, but I don't really see a way around this as long as the blockchain is an open ledger... any solutions?
Send them to an address that has a lot of coin, then withdraw in different sized amounts
Exchanges, for example, maybe change coin types, do some trades if it makes you feel better.
Mixers
direct exchange to anon coins like monero using, say, shapeshift followed by back to xbt in another exchange.
All of the above make things pretty onerous for even resourcefull trackers.