http://www.ffcompendium.com/h/incross.shtml
That should answer any questions you have, but to summarise:
Character Crossovers
Several character names make appearances in many FFs. There's been a Cid in every Final Fantasy (excluding MQ) since FF2. These Cids are usually old, brilliant men who frequently control the airships. Cid was playable in 4, 7, and Tactics (Cidolfas Orlandu, also known as Thunder God Cid). There's also a Doctor Sid in TSW. As well, characters named Wedge and Biggs have been in 6, 7, 8, 10, and TA (and also have cameo roles in another Squaresoft game, Chrono Trigger). There have only been two real character crossovers in the FF series: Cloud from 7, who reappeared as a playable character in Tactics (Aeris also appears there but is only called the Flower Girl), and Gilgamesh from 5 who reappeared as a Summon in 8. He also appears in a few places in 9, where he's also called Alleyway Jack. Gogo, who appeared as a boss in 5 and a playable character in 6, is nevertheless two different characters who only have two things in common: their propensity to wear loud clothes, and their Mimic class. Perhaps they're distant cousins.
Two cameo crossovers go to Lone Wolf, the thief, who's behind bars in both 5 and 6; and Boco the Chocobo, who's Bartz's buddy in 5, is the Chicobo belonging to Squall in 8, and who's rescued by Ramza and Agrias in Tactics. CSW Khan mentions that the Japanese "initials" (first syllables) of Bobby Corwen, the Chocobo in FF9, is "Boco".
Hyne, the sorcerer bad guy in FF3j, is mentioned as the "father of sorceresses" in FF8 in a completely different context. It just possibly may have another crossover in the form of General Hein from FF: The Spirits Within (they're pronounced the same).
As a minor side point for other Square fanatics, Lucca from Chrono Trigger is in Lahan Village in Xenogears, as well.
As well, a few things not mentioned on FF Compendium, is Hilda, who appears as the Phynn princess in FFII, and is Cid's wife in FFIX. Also, there is a Sarah in FFI, III, and IX which is a spoiler which I won't go into details about. Incidentally, there is also a character named Jane in FFI and the FF movie.
Finally, besides appearing in FFV, VIII and IX, Gilgamesh also shows up in FFXI Online as well, in a totally different form from his previous incarnations (like Sarah in FFIX that too is a spoiler which I will not elaborate on).
Hoepfully this has helped.