First, vassals are forced to give you resources or a war is declared. However, since I usually vassalize them with only a few cities left I'd rather trade them resources instead of demanding them. If I can get them to trade techs again so much the better.
Second, you can control the research and its attacks: as bardolph said, go to "I'd like to discuss something else...". If you're at war beside the research option you can also tell it which city to attack. Granted, he may not conquer it, but he might put up enough of a fight to hold some of your enemies troops tied up. Controlling research is useful even if you can't trade as he'll never beat you to any tech that gives a bonus if researched first. You can also pay him not to trade with your enemies and you'll at least be certain they don't get the techs you trade with the vassal.
As for the UN, a vassal is forced to vote for you in the elections. Having vassals on the other hand may make the other civs less inclined to vote for you, so the effects are mixed. If you're lucky to be friends with an overseas AI (no "close borders tension") then the having vassals demerit won't count for much though. I assume by the time you meet them you're also running Free Religion if you go for Diplomatic, so no religious demerit from overseas.
If you're going for Domination/Conquest having multiple vassals really speeds up the game. It's not just that you finish wars earlier; the combined powers of two civs (especially when one's a vassal) may not be much, but wait until you have two or three vassals! Here's a Domination victory full of vassals:
Tokugawa domination.