What Constitutes Christianity?

On his blog today, Al Mohler takes issue with some recent comments from Joel Osteen: Does Joel Osteen Not Know, or Does He Not Care?

Mohler:

Joel Osteen is in the news once again, this time for saying that Mormonism is just another form of Christianity.

The main point of concern in Joel’s latest comment is the lack of any biblical standard of judgment and the total abdication of theological responsibility.

He doesn’t “get hung up” on doctrinal issues, nor has he “really studied them or thought about them.”

Not to heap criticism on Osteen, but Mohler is right that all Christians need to think deeply about what constitutes Christianity, and what beliefs separate authentic Christianity from non-Christianity.  We are constantly bombarded with different ideas about what “Christianity” should look like.  Are these different ideas just different opinions from various Christians, or do some of them deviate from actually being Christianity?