About garuda she was first seen into FF11, but well don't forget that the game at the start was under Tanaka control and he was from FF11, a lot of the work on Garuda was already done probably then they have use her. outside this, if you look at all the trial added, they are the most know and present of the summons (will not count FF14):

- ifrit : 8 games
- Titan: 6 games
- Ramuh: 7 games
- Shiva: 10 games
- Leviathan: 8 games

some of this number can be almost doubled with the game not mainstream, like the FF7 crisis core, FF12 revenant wing, FFT,....

ps: Alexander only 6 games ^^

source: http://finalfantasy.wikia.com/wiki/List_of_Summons