Can trading be done on coinbase.com? On coinbase.com I tried to sell some bitcoins and was told I had to register a bank account.  I'd have expected that only if I were trying to withdraw dollars, euros, etc., from coinbase.  On mtgox one can sell bitcoins and have dollars in one's account.  Is that impossible on coinbase?  If so, how long does it take to move dollars to coinbase from a bank account and buy bitcoins?  If the price of a bitcoin goes up to what looks like an absurdly high price and I suspect it's a bubble that will burst, I might want to sell bitcoins and then 12 hours later, buy more at a lower price.  But if it takes a few days to get money back and forth between coinbase and a bank account, and it that must be done in order to do such trading, then coinbase is not the place to do it.

So what can and cannot be done there?
Coinbase unlike Mt.Gox is not a bitcoin exchange, it is a bitcoin wallet with the option of buying or selling bitcoins using a US bank account. You can store bitcoins on the site but not USD. 

This is primarily done for legal reasons. When you allow people to trade currency with each other instead of just being a currency dealer you open yourself up to a whole world of regulatory problems. Namely people would have to be extensively verified and new anti money laundering systems would have to be put in place to comply with FinCEN.