I'm astonished to see Vox on so many people's lists. Aside from airing a little dirty laundry, they really didn't have an impact on anything. I suppose most of you are considering their role in the break up of the Continuum, but that bloc broke up due to internal tensions between signatories (unrelated to Vox). The weakened remnanst of the bloc was then seized by the Karma coalition. Vox had very little impact on anything in my opinion.
I would agree with NPO/MK (in that order) at the top of the list. The two most dominant and influential alliances of all time and their rivalry has shaped the world.
After them, I would say the Polar/TOP relationship has been the biggest driving force in world politics. Dating back to the Unjust war where it first sparked, it has played an important role in pretty much every war since. The rivalry eventually lead to the War of the Coalition, it was one of the prime causes for the tensions between Citadel and NPO which had a big role in Karma, then bipolar happened, then the bye-polar war, then the Polar/TOP treaty was a major factor in the rolling of NG/NPO/etc last year, and Polar/TOP seemed to be the main targets of this latest war in response to that. Polar were especially influential early on under Ivan and antagonist extraordinaire Sponge. TOP also played a large role in the formation and lasting stability of the Continuum.
Last one of the top 5 is tricky. GOONS were the original bullies/lulz alliance and played a major role in forming the raiding/might makes right arguments that are still relevant today. The unjust war was also a huge deal. Gremlins took nation building to a new level and were very influential as the moralist/principled alliance. Umbrella also deserves a shout here as well.