Usually I end up picking several techs to focus on during the game. What techs I focus on is usually dependent on my Leader, Civ's UU, the terrain, my infrastructure, and the victory condition I'm aiming for.
If I'm an industrious leader, then a lot of the time, I will try to pick out a few wonders that I think will help further my cause, and then research for them. For leaders that start with Mysticism, I usually end up making a push for Polytheism (Hinduism).
Also, if I'm playing as Caesar, I usually end up making a fairly early push to Iron Working to allow me to build Praetorians. Similarly, with the Mongols, I end up making a push for Keshiks. Generally, I try to focus on getting the tech for my UU as soon as possible so that I can sustain their production for the longest possible time. Usually after I get a civ's UU, I stop military research until my opposition starts getting into a position where their military technology is equivalent to mine. This sustains my UU advantage for as long as possible.
The map also heavily affects how I research. On terra and continent maps, I usually make a generally strong push to acquire Optics and Astronomy relatively early for the Caravels and Galleons, respectively. If the map is particularly water-heavy, I may end up going and getting Frigates as well. On plains maps, I try to pick up horse-based military techs.
My infrastructure also forces a lot of my tech decisions. Picking up bronze working is particularly important in the early game for the benefit of increased production by chopping forests. If there are some luxury resources around that require a plantation, I try to pick up calendar fairly early. Wines require Monarchy. Animal Husbandry helps with cows and such. Hunting allows camps. Agriculture allows farms. Production can surge with a late game push towards Assembly Line followed by a push for Plastics to create the Three Gorges Dam to provide power to all of those Factories.
My decision on how to win also significantly affects my tech decisions. If I'm going for a Space Race victory, I like to beeline for whatever tech enables the Space Elevator (+50% spaceship production) after I get Rocketry (for Apollo Program). For diplomatic victories, I like to beeline for Mass Media to produce the UN. For domination/conquest victories I like to try to pick up Flight (fighters), Radio (bombers), the tech for infantry, the Pentagon, and tanks, before going for composites (for Modern Armor). I'm not particulary good at Culture victories, and haven't had one thus far. So I really can't give advice on that.
Other things I think about are the following...
If I have a 5xp unit, I like to go for Military Tradition quickly (for West Point).
Combustion is important late (for Oil).
After my initial research lines are complete, I like to go for Liberalism (free tech) and Economics (free Merchant).
I change the leader and map type often so I can't give you any hard and fast rules for researching. I've found that most of my research decisions are made on the fly in the face of my current game needs.
Hopefully the above hodgepodge of suggestions and ideas helps you a little bit.
-MM
