1. Street Registration. This is the default option. It's good for trading because it has the lowest cost and most liquidity, but it does allow your broker to sell your shares and keep the proceeds, thus introducing significant ownership issues if your brokerage firm defaults.
2. Direct registration is the option that lists you as the owner of the security with the transfer agent. This protects you against hypothecation (your broker selling your shares and keeping the proceeds) but is not as liquid and not really feasible for trading.
3. Paper certificate is the third option. Not every broker and not every security offers it. It costs the most and is the least liquid, but provides the security of "touch value" that some prefer.