Some largely long-term thoughts:
1) Separate out the philosophy-type techs from the actual technologies. Ideally, these should work from a totally different system. The number of prerequisites for them should be more limited, and they should be gained semirandomly instead of via research (Great Prophets could perhaps spawn them on generation, along with a religion?). They would also spread between trading partners fairly rapidly, being much less faction-specific than actual technologies. In some cases, of course, they should still retain prerequisites, when their implementation would be completely hypothetical without a certain technology, or when they aren't logical without certain antecedents (e.g., socialism stemming from the wide use of unskilled labor in factories).
2) Put less emphasis on "liking you" in diplomacy. All nations should be self-interested enough to give almost anyone almost anything in exchange for a good deal, short of actual wartime conditions.
3) Add more diplomatic options, and have fewer of them contingent on technologies. Unilateral protection agreements come to mind, but I'm sure there are others.
4) Allow any diplomatic option to be traded for any other.
5) Eliminate the seemingly baseless hatred that some factions have for each other. If two factions aren't at war and haven't been at war, they should have no objections to anyone trading with the other. (Possibly later on more sophistication could be added for Cold War-type conflicts, but those should be corner cases.)
6) Technologies should gradually spread between factions even without direct trading. The probability per turn of spread would depend on a) strength of relationship between the relevant factions and b) an index within the tech itself (Writing would have a very high index, for instance, whereas Fission would have a very low one; in general, they would depend on the degree to which the tech could plausibly be kept secret).
7) "Future Tech" should ultimately be removed and replaced with some actual possible future technologies.
8) The Alpha Centauri win condition should be ditched and replaced with the condition of learning super-advanced techs such as Universal Nanoconstruction plus Artificial Superintelligence or the like, which would make you so powerful that actually conquering the world would be a formality. Seriously, who cares about Alpha Centauri?
9) The tech tree should, in general, be much more flexible, so that you have more options at any point, but those options should perhaps take longer. Ultimately, combined with #6, this would mean that most technologies would be obtained through gradual leaks or other cultural interchange, rather than through direct personal research.
Now some more specific and readily implementable suggestions:
1) Until #1 in the general suggestions is implementable, all philosophical or "idea" techs should be removed as prerequisites for anything (except other philosophical techs) and have their research costs and effects sharply reduced. These include: Mysticism, Polytheism, Meditation, Monotheism, Priesthood, Monarchy, Code of Laws, Theology, Civil Service, Feudalism, Philosophy, Music, Literature, Drama, Guilds, Divine Right, Education, Liberalism, Nationalism, Military Tradition, Democracy, Constitution, Corporation, Fascism, Communism. Most of these should have their prerequisites removed, too, or at least most of them.
2) Here are some examples of what the prerequisites should be for certain early technologies, as #9 above (I have reasons for all of these if you want to hear my reasoning).
Hunting: None, and all factions should start with it (we're talking pre-Stone Age here―how could any society have eaten before the Green Revolution without hunting, just foraging?).
Polytheism, Meditation, Sailing, Pottery, Animal Husbandry, Archery, Monotheism, Writing, Monarchy, Drama, Code of Laws, Currency, Calendar, Civil Service, Philosophy, Music: None.
Bronze Working, Masonry, Iron Working, Compass: Mining only. (Magnetic compasses can be constructed using lodestone or other materials that are not, strictly speaking, iron.)
Priesthood, Theology, Divine Right: Mysticism OR Polytheism OR Monotheism.
Literature, Mathematics: Writing.
Metal Casting, Machinery: Bronze Working OR Iron Working OR whatever Aluminum harvesting requires. (However, Machinery and/or things requiring Machinery will be far more expensive without Metal Casting.)
Feudalism: Monarchy.
Optics: Machinery.
Engineering: Mathematics.
Paper: Writing. (In principle, you can make paper without knowing how to write, but I can't think why anyone would think of it.)
Guilds: Not quite sure. Your civ should have to have divided labor for guilds to exist, so it should be sometime in the Classical period at the earliest, but I don't know what a good prereq should be.
Banking: Currency.
Construction: Remove entirely, since it makes no sense.
Those are just the early techs, of course, but you can see what I'm driving at: a much broader tech tree. The current one is far too fatalistic.