Does it have to be 2D?
If not then Psychonaughts, Portal (if you call that a platformer) and Soul Reaver come to mind...

Psychonauts have many bottomless pits...


edit - for the clearest example, just think of the whole milkman level.

Good call. I don't think any of the "Kain" games had bottomless pits. They weren't 2D but I don't think that should matter; lots of 3D and 3rd person shooters have bottomless pits.

It's been ages since I've played them, but I don't think there were bottomless pits in Alien Carnage/Halloween Harry, Secret Agent, Alien Rampage, or Abuse. And I've all but forgotten what Jazz Jackrabbit and Earthworm Jim were like. Realms of Chaos, Bio-Menace, and Commander Keen definitely had bottomless pits and instant-kill traps (but pits were pretty rare in Bio-Menace). As for indie games, I like Alastair John Jack's Final Vision and Ainevoltas 2 for some easy-going platformer action.

Castlevania series (well, the metroidvania ones: Symphony of the Night, Aria of Sorrow, etc)

I've played some Jazz Jackrabbit and got a bit into the game, seen no bottomless pits so far but that could change later.

The Amazing Spider-Man is mostly action but has a lot of jumping/swinging around, haven't seen any bottomless pits in it yet either.

I'm pretty sure Abuse had a few. I distinctly (spell) remember falling off the screen and hearing the painfull scream.

I can't decide whether that counts as a bottomless pit or a topless sky.

TokiTori? AFAIK there are no bottomless pits. On the other hand, there is no jump option....

Classic Prince of persia 2. Has only one pit. But the game still manages to punish the gamer for mistakes.
grviper posted short description and link for walkthrough videos:
http://www.gog.com/forum/general/release_prince_of_persia_the_two_thrones/post54

Don't think it did. Actually I think every 2d Metroid didn't have any bottomless pits (Haven't played Metroid 2 though) Same with Symphony of the Night and most of the 2d Castlevania games after it.

So.....pit with instadeath spikes/instadrown water/instasizzle electricity....is that considered bottomless since there's no way you hit the bottom and survive?

If we mention psychonauts, I remember being rather miffed at the meat circus, I believe it's one of the games where I wish there were more bottomless pits. At least with a bottomless/instadeath pit you die and if you're not out of lives, respawn a bit back, whereas if you have a non-bottomless pit (like Metroid style games), you fall down and then have half an hour's trek to get back where you were... I'd prefer death and respawn, or the Sands of TIme dagger to rewind and retry.

How about Abe's oddysee? Is that a bottomless pit? I mean, you fall down, you hear a scream, but then you also hear a thump and a screen shaking effect before you respawn. There must be a bottom to it right? ;-)

We could be talking more about it as a lazy game design choice? "There's a pit here. You fall you fail... no I don't know what it is that kills you but you sure die, so don't fall"

As for non-bottomless pit games (From memory) there's the likes of Yo! Joe! which I believe has no bottomless pit, just frustration at climbing back up.
Qwak and BubbleBobble and Parasol Stars and that kind of single screen platformers usually just put you at the top.

A Valley Without Wind doesn't seem to have any, but I got stuck in a cave I couldn't climb out of, so not exactly non-lethal drop.

Don't think the old Secret Agent Man games had bottomless pits either.

And I'd like to nominate Flashback as "Bottomless pit...or is it" for ending level 1 wherein you throw yourself into a pit which seems bottomless unless you get the anti-grav device first. But there are other bottomless pits later.

Crystal Caves has no bottomless pits as fas I can remember:
http://en.wikipedia.org/wiki/Crystal_Caves

Many "Metroidvania" style games don't have bottemless pits. For example, Castlevania SOTN, Super Metroid, Knytt Stories, Shadow Complex, etc.

Abuse has no bottlemless pits. There's always a way out of whatever pit you fall into.

Also, Iji's good.

Hurm. I'll mention some old goodies:

Donkey Kong 64 contain a few, but the design of the game ensures they are never more than a slap on the wrist. at worst you get booted to the entrance of the current level, which is no big deal because the levels are mostly designed as a series of hubs. At best you get kicked back to the start of the room.

Banjo-Kazooie only has one true bottomless pit that I recall. However, the game does use proportional falling damage, so jumping from a handful of very high places will kill you. No idea about the sequel.

Wario Land 2 and 3 are designed around the gimmick that Wario is invincible. That doesn't really make the game any easier, but...

Erm. I guess you wanted something newer? Can't really help you there, sorry. Also, Cave Story uses other instant-kill mechanics, so it's not a good example.

Metroidvanias (we need a better word for these) really can't have anything bottomless. One of the keys to them is being able to go anywhere (depending on story progression & equipment) over and over, backtracking, and limitless exploration. This doesn't really work if parts of the game world send you flying (or dropping) off to nowhere.