They each originally had their own intended purposes. .Com was for commercial organizations, .Net was for network infrastructures, and .Org was for organizations. They are all unrestreticted and no longer fall stricly under their respective categories. .Com is now the first extension that should be bought if available in all cases. .Net and .Org are often times now bought as a backup. If you buy "something or other .com", it is often times wise to get the .net and .org as well, if you are planning on developing the name. .Org is still a very good choice for organizations, but as I said, the .Com should always be bought if available.
You also have many more choices now that are even more specific. It is pretty obvious what .Biz and .Info are used for and may be useful in some instances. Country codes such as .US, .ES, or .CN can be useful. There are even now region codes you can get, .EU and .Asia.
It is always safest to get the .com and then depending on what you are going to do with it, then consider the other extensions you may want.