When playtesting games, you'll notice that different playtesters have a different approach to the whole thing. Here's an attempt to categorize those different types of playtesters (just for fun):
The ruleslawyer
This type of playtester delights in finding holes in your rules. During explanation they will ask a lot of "what if" questions and during gameplay they try to set up or spot situations that are not covered in the rules. Such playtesters can be annoying, especially when your design is still "rough", but the can also be very useful to make sure your rules become airtight.
The non-gamer
This type of playtester likes finding a strategy, preferably one that is simple to execute, that clearly breaks your game. It's very important to have at least one such playtester in your group, especially when you have a more complex game.
The player
This type of playtester just likes to play games, but is not particularly interested in the process of playtesting a game. These kind of playtesters can be very handy when you have a game that has already been playtested thoroughly and you are more interested in quantity of feedback, rather than quality, or when you just need an extra body to get the required number of players for a game.
The evaluator
This type of playtester will treat a playtest session as a normal gaming session, but will come up with a lot of feedback and suggestions when the game is done. Can be very useful, especially during the early stages of design.
The new kid on the block
These playtesters are often friends and family you roped into a playtest session because your simply desperate for playtesters. They might occasionally play games and perhaps they are even interested in gaming, but they won't provide you with the most in-depth feedback. Still, if casual gamers are your target audience their response to the game might be invaluable.
I'm sure you can define more type of playtesters!
- René Wiersma
I think this one bears note:
The Boardgame Nongenius.
A friend invites him to your playtest session, you invite a video-gamer friend to try board games, or a family member joins in.
Very similar to the "New Kid on the Block", the nongenius loves the game, but can't follow some of the most fundamental rules. He insists on providing feedback, but the suggestions defy the very concept of your game.
Expect to meet him if you attempt playtesting on the internet, or if you run a complex/rules heavy game.