1)
More in depth diplomacy. I'd love to be able to make truly complex deals, and have the AIs try to make them with me. For instance, let me contract out civs to do tasks for me. Lobbying the other side for trade, paying them to research a tech for you, and issuing diplomatic requests ("Move that goddamn influence starbase or I will!") would be nice... as well as more "under the table" kinds of deals, like slipping an AI money to cripple a civ with espionage, or coordinating with them to get them to effectively aid in your surprise attack... or lead them into a trap!

It'd also be nice to be able to put additional pressure when making a demand/trade: accept, or we WILL declare war on you.
2)
Better United Planets. Being able to set the agenda, consult with others to see how they'll vote (and if you should be buying their votes), as well as simply making the UP more influential. As it is, the effects of a resolution are rarely game altering and meetings are too few and far between to make a difference. It'd also be nice to see things like "peacemaking" missions, or "liberation" resolutions, where either war or tribute to the fighters is mandated of all UP members.
3)
In depth ship design... I'd love to see more variety in the ships, and more strategy in how they're designed and used. Targeting modules (increase minimum damage per shot), evasion modules (the opposite), modules to allow you to convince ships to attack other ships first (ie, make your ship look more/less dangerous by comparison), cloaking device, anti-cloak sensors... and that's all just off the top of my head. Even more options would be available if you extended the rules of the ship combat, or got rid of the rule based system entirely and moved to simulation (without tactical control, of course!)
Its nice that we can make the ships look however we want, but it'd be nice if they could ACT however we want, too!