I haven't played all of the FF games, but from what I can remember, summons have been utilized in about 3 different ways:
1) They appear for one attack and then disappear (FFVI)
2) They replace the entire party and become controllable (FFX)
3) They replace your other party members except you and fight alongside you but cannot be controlled (FFXII)
I think summons are best utilized based on your needs and how you like to play. When I played FFVI, I always used them during boss fights - either as an opening move to shave off large amounts of HP thus making the remainder of the fight easier or as an ending move in the hopes that it would be the final attack needed to kill the boss. When summoned, they were in and out and didn't take you away from the action. The only thing I found was that although they were important to the story, they kind of lacked presence, maybe it was because of the SNES 2D graphics at the time. They were beautifully drawn, but I guess they were missing the oomphf that could make me go "WOW".
When playing FFX, I mostly used them as meat shields and it was great to be able to control them for the first time. They were important to the story, had fantastic designs and had presence. And with the introduction of 3D graphics as from VII, summoning and attack animations took a lot longer. It's nice and pretty to watch the animations once, but after continued use, I found that this took me away from the action for too long. Sometimes that made me not want to use the summon because I'd have to sit and wait for the summon to wrap it up and go (I'm looking at you VII). If I remember, I think FFX had an option in which you could shorten the summon animation, which helped a lot to get me back into the fight.
I found the summons in FFXII to be utterly useless. I used them once, learned how terribly they adapted in battle and never used them again. They would attack enemies that I didn't need help on or they'd die really quickly because of they'd make dumb decisions based on their gambits. Maybe I didn't know how to properly utilize them, but I relied mostly on the quickenings as a substitute for the summons.
Although the game hasn't been released yet, I can already tell that FFXV is going to be the game that best utilizes it's summons - both in gameplay and presence. I didn't play the Duscae demo, but from what I could tell, you could only summon Ramuh when you were in danger. I really like that because it forces you to fight battles by yourself instead of spamming summons as an easy way out. And only when you are in serious trouble, can you summon an Astral as a last attempt at survival. I hope this mechanic stays in the final game. Although FFXV is a gorgeous game, I like that SE didn't go too crazy on the animations for the summons. I've only seen Ramuh and a bit of Titan, but it didn't take too long for them to enter the battle, do their thing and leave which was nice.
In terms of presence, I think FFXV gets everything right. Firstly, they're hella important to the story and secondly, they are HUGE. Just the sheer size and design of these Astrals give them that wow factor and remind you that that's not a meat shield, that's a GODLY SUMMON that could save you in your most desperate situation...