Right now, it's a decision heavily influenced by price. Most common brand: probably Ajax. (I might have tried it first because of Ajax praise from one person here.) But I have also bought Dawn (on really good sale) and recently got the cheapest Fred Meyer/Kroger home brand (99cents for a big bottle), which was probably not the best detergent ever, but worked OK for my needs.
I have heard arguments that better detergents are better values because they go further. But I hate washing dishes so much that I tend to do a lot. I'd rather do it more often, and have it done faster, than do it once a day and face a depressing mountain of dishes. Thus, cheap detergent probably is good enough.
In the past, I had a period of using "green" detergents. I think they might be easier on hands, and the scents are certainly nicer. But the price is too much for me now.
I also have had a tendency of changing brands just "for something different." I'm doing that less, now, since price has become #1 concern, and Ajax is always cheap.