Red curry paste is the most common of all the curry pastes. It is used widely in many dishes that you are familiar with such as tod mun and satay. Red curry paste is a mixture of dry chili pepper, shallot, garlic, galangal, lemon grass, cilantro root, peppercorn, coriander, salt, shrimp paste and kaffir lime zest.

Green curry paste has the exact ingredients as the red one with the exception of the dried chili pepper. Fresh green pepper is substituted.

Yellow curry comes from Southern Thailand and is similar to red or green curry, but it is made with yellow peppers and turmeric.

This is also known as matsaman and/or massaman

Masaman is an Indian influenced curry. Masaman curry paste has several Indian spices such as cumin, cinnamon, cardamom and cloves. When sold in Thailand, you can see whole white cardamom pods in the paste.

This is also known as prik pao and/or chilli paste soya beans

This is a brown paste I buy in Thailand or prepare in advance and keep in the fridge. I've kept mine in the fridge for months. It is available here in the US in Oriental groceries in glass jars.
There are many variations of this, but the core mixture is: shallots, garlic, shrimp paste, dry chili pepper, salt, and sugar. Frequently there is also tamarind paste and dried shrimp.

This curry paste is a mix of shallots, garlic, lemon grass, galangal, gra chai, pepper, salt and shrimp paste.

It normally comes in a little plastic jar. If you keep it in the freezer, it stays good virtually forever.