KINGDOM HEARTS I & II
During Kingdom Hearts, we are first introduced to Aeris. Though it seems to be the same girl from Final Fantasy VII, it seems as though this one's actually part of a different world. This Aeris' story doesn't seem to be too similar to the same as the original, for this one only knows of the story of the Heartless and apparently lived in Hollow Bastion, which is originally called Radiant Garden. Later, we're introduced to Cloud, who fights with Sora in the Coliseum. He later tells Sora about how he made a deal with Hades about finding someone. Seeing as how Hades is the God of the Dead, our immediate prediction is that Cloud was looking for Aeris. But seeing as how the story in Kingdom Hearts is different than the original, we don't have exact proof on this, or whether the Aeris he's looking for is the same one Sora had met earlier in the game.
 

There's also apparently talk of Cloud finding his "light". Most people concluded that his light was Aeris. I used to think so too, until I played Kingdom Hearts 2. When Cloud talks about finding his light, I really don't think it's too metaphorical. I can honestly say, I don't think it has to do with Aeris. The two apparently "reunited" at the end of the first game, when Cid brings Cloud up to the other FF characters. Though it's not confirmed if the two had somehow known each other before, the two do walk up to each other and stare as if there was some sort of connection there. But even so, during KH2, Cloud was still looking for his "light" even though he had met with Aeris again. I believe by "light", he meant getting rid of his mysterious dark past, which, like the original, has some connection with Sephiroth. And when Cloud was talking about "looking for someone", he probably meant Sephiroth, who he was searching for in the second game. Tifa also seems to be part of Cloud's past in this story, trying to help him find his "light".
 

Even though Aeris isn't that "light" everyone thought Cloud was looking for, she still seems to be the guide and friend that stands by his side. During Kingdom Hearts II, Cloud speaks of leaving, not wanting to have her involved. He says he'll eventually come back, though she says he didn't seem so sure, but still says that she knows that after finding his light, he'll come back. He replies with a casual "I suppose", but we all know that's just Cloud-speak. Apparently there seems to be a Kingdom Hearts 3 coming to us in the future. Nothing has been  said about the game yet, but after Cloud and Sephiroth disappear into thin-air in KH2, it seems his story in this game might still end up continuing, so we can find out of what occurs between him and Sephiroth. Hopefully, Aeris will still remain to be a part of it, as well.

FINAL FANTASY TACTICS
Though I own this game, I was never really good at it, so I never got too far in it, except for a little forward in the beginning. Because of this, I've never actually met Cloud and saw his short part in the story. However, I have read online of what occurs during the game. Cloud seems to appear out of no where in the world, with talk of the promised land and such. Though no one seems to understand, he runs off and meets with a girl, who seems oddly familiar to him. This girl asks if he wishes to buy a flower for one gil, which brings "deja vu" to both Cloud and the players of the game. Cloud runs off again, but rescues the flower girl, coincidently also named Aeris, from some men who come to bother her.

It's rumored that when Cloud was in the lifestream in Final Fantasy VII, he ended up going to the world in Tactics, where he meant Ramza and the familar flower girl, while he spoke of finding the Promised Land. This isn't exactly proven, but it all seems to tie in together, and does seem to be an interesting puzzle piece that seems to fit well.