How about the idea of joint research ventures?
For example:
Let's say there are 5 civs. Civ A and B are ahead of you in research (they've achieved feudalism), and are threating your borders. You can research feudalism, but it's going to be 25 turns away.
Civ C and D are friends of yours; neither of these Civs have feudalism.
So what do you do? Well, normally you would try to:
A) Steal the tech
B) Ramp up the economy and try to buy it
C) Hope you don't get attacked any time soon
D) Go ahead and obliterate Civs A and B
How about this? Let's reward those who are kind to their neighbors by allowing joint research projects, so that Civs C, D, and you can join together to research one tech more quickly.
In this way, Civs can pool research efforts if they have a clear trade route. Research is shared in the form of "Research per turn" just as gold is. When the tech is researched, the deal is cancelled, and all Civs involved in the project receive the tech.
Now you might be thinking, "Wait a minute. That means I could contribute only 1 beaker of research per turn and get a near freebie?" Well, in theory, yes. However, both human and AI players would require some sort of compensation for your lack of research contribution, so this balances out. Also, if this is the case, it would be no different than someone just giving you an advance, which I haven't seen happen too often.
Where this would really shine is the above scenario, where getting one particular advancement is of critical importance. Where you would take 25 turns to research, it would take all 3 of you 7 turns for your joint project. You will be able to build those pikemen for defense much earlier on.
This adds a whole new dimension in long-term planning: as you could really focus on particular branches of the tech tree, at the detriment of being limited in other areas of research.
The overall time of research would remain the same, as this is the time equivalent as you researching one, C researching one, D researching one, and then trading each other for the missing advances. However, instead of trading the advance, you're trading the beakers needed for the advance, which allows 1 advance 3 times as quickly, rather than 3 advances at normal speed.
The catch to all of this: all participating civs must be able to research the target advance. If Civ D cannot research feudalism, then D cannot contribute toward the joint research project.