I've always enjoyed UN / Galactic Council / Whatever bodies in the various games in which they appear.
The only thing I've never truly liked about them is that the interesting proposals are completely computer generated. Why can't, for instance, *I* propose an act which increases everyone's trade caps (and makes everyone's spy insertions somewhat easier)? How come I have to wait for the computer to propose it?
Additionally, many of the more modern takes on the idea allow vote bartering of some form or another. I've never particularly like most of these, either.
GalCiv has one of the better systems, where influence points are accumulated just like currency, and therefore giving away 100 IPs permanently reduces my voting power and increases yours by the same amount. The amount of influence people are willing to trade is just never very high, though, and with your Influence reserves growing all the time, it's hard to, say, set up a voting bloc large to make sure the next Galactic Election goes your way without just getting 51% of the votes organically. And it's also not possible to get the Kor to give you all of their votes just for the upcoming election.
Similarly, most games don't give you enough time in-between announcing a proposal and requiring your vote to go out and electioneer. So, if the +Trade / -SpyDefense proposal comes up, and I really, really want this to pass, I don't get a chance to go to my friends and say, "Seriously - how much will it cost me to guarantee that you vote yes on Prop. 6?"
EDIT 2:
I could have made it clearer above, but I really, really like the idea of vote bartering. I'm just not 100% enamored of how it's been implemented so far. 
EDIT:
And another thing. MOO3, I'm looking at you. MOO3 had this great idea for a bill you could pass in the Galactic Senate. It was called the "Praise So-and-so" bill, and, basically, it raised everyone's relations with the So-and-So empire. Great idea, right? Unfortunately, the only people who would ever vote yes for it are the ones who already liked So-and-So.
Which made it rather ... useless, since you couldn't get the Senate to vote to improve relations with So-and-So unless the majority of the Senate already had good relations with So-and-So, at which point you don't need the bill.
Ditto, reversed, for the "Condemn So-and-So" bill.