Is it legal to trade bitcoins on coinbase/mtgox in the US? I am just wondering whether it is legal to trade bitcoins in the US just like we do for stocks? I see similar legal questions about selling OTC, but I am more interested in buying and selling in well known exchanges like coinbase/mtgox etc. Can I just trade them like normal stocks, as long as I pay taxes? Or do I need to register with FinCEN to trade?
Commodities exchange, yes.  Stock exchange, no.

Stocks are securities, so it wouldn't be appropriate to trade bitcoin on a stock exchange because they don't have any relation to the assets or liabilities of an underlying company.  Bitcoins are valuable (or not) only intrinsically.  This is closer to a commodities exchange, which is what CEX.io does and previously Mt. Gox did.

This is equivalent to trading gold, wheat, pork bellies, platinum, and so forth.  People on a commodities exchange can buy and sell options and forwards.  Which is economically a perfectly appropriate thing to do for an asset like Bitcoin.

As of right now, the legal situation is still confusing to the government, but this article argues that the CFTC does not regulate bitcoin trading even though it's a commodity.  FinCEN thinks that people who sell BTC for USD will presumptively have to register.  You will have to work out for yourself what rules might apply to BTC traders, if any.  I cannot provide much help on this front.

As a general tax rule, you need to observe Notice 2014-21 treating BTC as non-currency property and will have to report your transactions.  If you are buying and selling as a business, rather than holding BTC for anticipated appreciation, then you will need to file Schedule C and maybe create a business entity.  If your money comes from appreciation and long investment, then you are an investor and can make use of capital gains treatment.  If your money comes from quick trades and the short swings of the market, then you are a trader and if your money comes from charging other people fees to make their trades for them, then you are a dealer - either of which is a business that must be taxed at the less preferential ordinary income rate.  Remember to ignore any tax reporting on "currency gain" or loss from BTC, since the IRS says bitcoins are not currency (but if you trade in other currencies, that's a different issue).

Selling bitcoins is taxed like buying and selling other property.  It will be taxable accordingly as a basic IRC §1001 transaction, where [gain] = [amount realized] - [cost basis].