I am engaged to a girl who is also LDS. It would be very tough for me to marry a girl who wasn't LDS for many reasons.
These are not all inclusive, nor are they in any particular order
1. Standards. I want a partner who has the same standards as me that can help me be an example to them. (not all LDS girls are this, and not all non LDS girls are this, but it is more common.)
2. I have a belief in what I live and want to teach my kids those same principles. I want a wife who helps me teach them this.
3. I believe that the only way to live with your family through eternity is through a temple marriage... I want that.
There are many other reasons as well but these are the main ones.