Ifrit, I think, can't be killed off story-wise; you just beat him down like any normal boss and he'll rejoin you. Titan is another such "freebie", at least in the fight itself: you can't actually defeat him until after saving/killing Ramuh and rescuing Porom, as he'll just keep Gaia's Wrathing you out of the fight unless Porom is there to cast Float.
Shiva and Ramuh both can be killed by mistake. Once they've been knocked down to a certain level of health(in Shiva's case it has to be done with a fire spell; I recommend simply casting Firaga with Rydia or Golbez and having everyone else defend/heal), stop attacking and wait for them to regain their senses. If you hit them again after the cue from your characters, they'll keep attacking until they or you die. The Sylphs can also be killed off, but all you have to do to avoid that is not speak to them(and if you engage one by mistake, you can just flee).
Later on, Asura and Leviathan will either be saved or killed depending solely on whether or not Rydia is in your party when you face them. And if you fail to save one or both of them, you'll end up forced to kill Bahamut when you face him.(And you must face Bahamut with Rydia in the party no matter what; if you don't, he'll immediately wipe you out with Megaflare.)
The only real effect any of this has on the story is dialogue differences; there's no real "bad ending" or anything such for failing to save them. --- Only the dead have seen the end of the war.
What he said, but if you are doing the bestiary entries then you will need to actually kill Shiva, Ifrit and Bahamut. For Bahamut all you need to do is kill either Asura or Leviathan while Rydia is not in the party to kill them off.
Bahamut comes too late in the game to really be of much use. Leviathan, while not as powerful, does give you decent opportunity to use. The 9999 damage isn't too facinating anymore if you've got the right party that can do that as well...and faster.
It doesn't take much extra effort to NOT kill the perishable summons anyhow. Do you WANT Rydia to be sad? They are her friends, not "mere pawns of power". Now just where have I heard that quote before?