Mining + Agriculture are the two most useful starting techs. You can go right for bronze working and animal husbandry.
I had thought about starting this poll recently as well. Great idea.
I agree with Bonafide's assessment. I would add that I like getting a worker out first or second, and both these techs allow my workers to get to the work on important improvements as quickly as possible and usually stay busy so as not to waste time. Also, if I am going for the Pyramids and/or the Great Wall, having Mining allows quick access to masonry as soon as needed. I play on Monarch level.
My second favorite is Hunting + Agriculture since I find Agriculture slightly more important than Mining as a starting tech, and it allows me to start with a scout for the chance at an early Goody Hut technology, etc.
Still though, having the Wheel is nice for early roads, and I have enjoyed that a little with the Sumerians. I may be wrong, but I tend to neglect the Wheel quite often while I am researching targeted techs, so starting with it absolves me of the responsibility of stopping what I am doing to research it at some point.
I've tried Romans as a civ starting with Fishing; and although the Praeotorian is fun, I find the Fishing start useful less often. Even if you happen to start with some seafood nearby, fishing is so fast to research that I still prefer Mining + Agriculture.