Is there any way I can find out the number of posts I have edited? I can not find it in my profile page. I think it is good to have a counter similar to votes/badges counters.
At the moment, there is no way to tell how many edits you've made. There was a question over on Meta Stack Overflow about this back in July 2009 which pretty much says the same thing.
Jeff seemed to hint at some kind of visible counter in his answer to that question, but enough time has passed that I suspect they've forgotten all about it, which is unfortunate.
There might be some queries over on data explorer, but they should only be used as a guideline as the data is not live. Also, they might give you inflated edit counts as they count retags which don't count towards editor badges.
As Ben said the data at our Data explorer is not live, but in so far that it is up to date you can use this query.