What are examples of third parties?

There are essentially four types of third parties, and they are distinguished by their motives for being so.

First, there is the "spoiler." They are the ones who became as outcasts in their original party and so created their own to "spoil" their old party's chances at winning by taking away votes.

Second, there is the "splinter." They simply break off of one of the larger parties because such parties didn't represent their ideas and beliefs.

Third, there is the "ideologue." These parties have a world view unique to themselves and so feel strongly enough to create their own party based on it.

Lastly, ther is the "protestor" or "single issue" party. These ones form on the basis of an issue or issues.

So those are all of the types of third parties (to my knowledge).