mattador101: ...

Matewis: Neither would it probably be worth it to research masonry before animal husbandry for the pyramids if you have several horse, pig or sheep resources that your workers could upgrade.

The holy grail at the start of the game is to build the oracle before anyone else, and to make sure you have monotheism and writing researched by the time oracle is finished. Then you will be able to select Theology as your free tech, which is a very expensive tech at that stage of the game. So it will give you a massive research boost and propel you into the next age. You also found Christianity in the process, and the religious buildings following from it can net all kinds of culture/research/money bonuses later on.

ConsulCaesar: Some crucial techs paths:

Economy: possibly the most important tech is Currency, which not only allows to build markets, but also grants a new trade route per city. One of your objectives in the early game should be to reach this technology before your economy crashes due to raising city maintenance costs. Other modifier buildings are grocers (at Guilds), banks (at Banking) and the Wall Street National Wonder (at Corporation).

Science: first Writing (for libraries and their scientist specialists) and Alphabet (which enables tech trading), then Education (universities and Oxford) and Liberalism (first to research gets a free tech plus new civics). After that, researching Scientific Method usually lowers your science at first, which sounds counter-intuitive, due to the obsolescence of monasteries and some ancient wonders, but it opens the path to many juicy techs that you want to have sooner rather than later.

Growth: your first technology choices should be to improve whatever food resource is available: Fishing for fish, Animal Husbandry for cows, etc. Later on, Civil Service allows chain irrigation (so you can build farms without freshwater as long as an already irrigated farm or city is adjacent) and Biology grants +1 food to farms. In the modern era, supermarkets (at Refrigeration) are another source of food).

Military: Bronze Working, Iron Working and Animal Husbandry reveal the ancient era strategic resources, which will play a crucial part in planning where you settle and how strong your army will be in the first part of the game. Then, Construction unlocks the first siege weapon (the catapult), which makes a difference when attacking cities with cultural defenses and/or walls. Defensively, Archery is completely optional but you may have a hard time with barbs if you decide to ignore it. In the Middle Ages, Feudalism unlocks longbowmen, which make even stronger defenders. Later on, Rifling unlock the riflemen, which are considered the biggest leap in strength by most players, and make the most efficient drafting unit (drafting is unlocked with Nationalism). You may also consider rushing towards the tech that unlocks your unique units (for example, Iron Working is a no-brainer for Rome).

Culture: the way leading to Music (including Writing, Aesthetics in the expansions, Literature and Drama) is where you will find the basics (libraries, theaters, culture slider, culture wonders). Music grants a free Great Artist to the first who researches it and unlocks the ability to build cathedrals, which with a +50% culture bonus are the most powerful asset in the way to a culture victory. To make use of cathedrals you will need several different religions, but it's not really necessary to found them yourself (you will need Priesthood for the temples though). The broadcast tower (with Mass Media) and the modern entertainment wonders (Broadway with Electricity, Rock & Roll with Radio and Hollywood with Mass Media) have the same effect as the cathedrals but you can't build as many and they come much later in the tree.

Space: the techs that allow to build spaceship parts, starting with Rocketry for the Apollo program. Surprisingly, Flight is a completely optional tech to launch the spaceship. Many players consider that the Space Elevator is not worth the time and resources it needs to be researched and built. Laboratories (unlocked with Superconductors, which are needed for the spaceship anyway) already grant a +50% spaceship production. Industrialism could also be considered a priority, as it reveals Aluminum, which doubles the production speed of the Apollo Program and some of the spaceship parts.