It kind of depends on how you want to play. In most Civ games, (5 included) there are distinct advantages to having more cities that generally outweigh the disadvantages, although the argument could be made that Civ5 has done a pretty good job of trying to balance these things.
So, if you're heading for a Cultural victory, you probably want to leave them alone, simply because conquering them is either going to be bad for your culture score, or bad for your economy/happiness.
Having a good set of trade partners can be important, especially if you have many extra resources to trade, but there's no distinction between trade partners who are on the same continent as you or on different continents, so I wouldn't think it would matter.
Personally I find that the more territory I control, the better my chances of victory are, and I tend to conquer anyone on my current continent. Waging a war by air or by sea is decidedly more difficult (especially if the opponents are AI), so I tend to have more of a chance to prepare in situations where my enemy is separated from me by water.
I also find that, especially in the higher difficulty levels, the AI is more prone to attacking me regardless of any shared history or previous successful diplomacy, so the faster I push them out of my area, the less of an immediate threat they are.