Google vs Microsoft
I don't mind Google sharing the browser market*, or the email client market*, or the productivity suite market* with Microsoft. Competition is a great thing for the end user. It was a lack of competition that resulted in the execrable IE6, or Windows ME.
What I really would mind was Google displacing MS at the top of the heap. That "do no evil" plaque is already looking tarnished, and a market dominance in areas other than ads would hasten its demise, I'm sure.
* Yes, I am aware that other products exist, but you know what I mean.