I think there is only one technology that I have researched in every game I have ever played without fail, regardless of my race, strategy, and start position. That is the repair bay. It is the tech to always research.
Aside from that (on the military side of things) you have the usual "vital" technologies regarding unit prototypes. You need a balanced fleet, and usually that means LRF, carriers, flaks, and probably a support cruiser. I personally am a huge fan of antimatter upgrades, but keep in mind I'm also love my capital ships, so I put those upgrades to good use.
For useless technologies on the military side, I'd have to say the Vasari technology that increases capital ship bombard range is probably the top candidate. It's ridiculously expensive for something that has virtually no effect. Not worth your time or money. The capital ship beam weapons are another dubious research; at least they do something, however.
Now, the civic side of the tech tree doesn't have very many "must have" technologies. I think ice and volcanic colonization are probably the most important in the long-run so you can claim those planets both as tactical staging points and for their resources. As Swordsalmon already mentioned, the population upgrades are a great investment and the low-level extractor upgrades are well worth your time.
Now, I could probably rant all day about weak civic technologies, but let me address an absolutely worthless one: pirate xenophobia. This ability reduces the strength of a pirate raid against you by about 10 or 20%. An experienced player probably already knows what I'm about to say, but I'll say it anyways. This pirate raid is still strong enough that I have to go back and fend it off. If I go back and fend it off, then this upgrade has effectively given me 10 or 20% less experience for doing so. In other words, this ugprade is actually a bad thing to have. It's one thing to be a double-edged technology (TEC insurgency can feed the enemy experience in the long-run, but at least it has positive side effects), but this tech seems to literally be a detriment.