Well aside from your own gear, it also depends on your class, and a variety of other things, such as raid dps (if it's low, the fight will take longer, so casters and healers are more likely to run out of mana), tank's gear (if he's taking more damage, you'll have to heal more, so you're gonna run out of mana faster), etc. I've taken two healers to Kara, a druid and a pally, both pretty equally geared, with mostly top-notch blues and a few PvP epics -- standard pre-Kara gear. The druid rarely has to pot unless the tank is really undergeared and getting his ass kicked so I'm burning through my mana trying to keep him up. The pally, however, -always- needs to chain pot during the longer boss fights like Moroes and Shade. His mana regen is a lot lower (healadin itemization is a bit more difficult), so even though he has 2000 more mana than the druid, he still runs out a lot sooner.

I guess one of the sucky parts about chain-potting is that not everyone has to do it. Some people have to shell out big chunks of gold before each raid (or spend an hour or so farming and brewing their own pots), while others just pick up a couple stacks of reagents and they're good to go. Seems kinda unfair.

As for elixirs and flasks, I've never noticed a big difference whether I use them or don't. The buffs must help, I guess, but they're pretty small in the long run, so they're more or less auxiliary. Organization is much more influential in the long run. At any rate, potion sickness doesn't affect elixirs.