There inevitably are apps that will do bad things (keyloggers, data harvesters etc).
It is important to watch what permissions apps are requesting and decide if you want to allow those apps on your phone.
Things to consider:
Do you know the developer (google, dataviz, twitter etc)
Devs that have a long history in the market vs. devs that have only a few downloads and little feedback. If an app has 250k dl's and no evidence of wrong doing has surfaced it is likely safe.
Does a tic-tac-toe game need access to my contacts? and the like
I do not believe there is a review process before apps are allowed in the market. If an app is found to do bad things they can be pulled.