See a lot of RPG and LARP here. We're mostly board gamers and have left a table a couple of times in the last 8 years.

We played a Descent type board game 1 vs many where they booked "DM" to 2 tables and you had to wait for them to do one table then the next. We talked to the other players at our table and let them know we wanted to leave, but were willing to stay if they wanted with no issues. Ended up they felt the same we did. We told the person running the game how we felt and they apologized and offered to try to find someone, but we told them we were done and left. 

This year we had a learn to play event and the 2 of us ended up on opposite teams each with a random person, not a big deal for us. The learn to play was staggered with another event by an hour so once we were an hour in the person running had to go teach another table. When you get into the meat of a game an hour in, that's not the time to leave new players. The random guys we were paired with then ended up arguing about every rule we didn't know, and we ended up leaving them at the table, with a "you guys don't need us to argue amongst yourselves." and we ditched.

Once three of us showed up to what ended up being 1v1 games so i was with a random person, not a big deal. The other 2 in my group quit half way through, they were playing together and didn't like the game. I stayed, even though i didn't care for it, because the person i was paired with really wanted to play the game. So i gave it my all and gave them a good experience.

I will always voice how we're feeling to who is running the game, if they are there, and if it effects another player will see how they feel about it and salvage it for them if i can. 

I have a thus-far unique game-abandonment story!  A year or two ago, I was playing in an OD&D game, along with two of my real-life friends, at a table of like 10 or so (I think the game was slated for 6 but the DM allowed generics obviously).  Perhaps because there were too many players at the table, because the DM was not this kind of DM, or because we were supposed to pick up on the nuance of it being an OD&D game in the pre-"amateur theater" style, well, as soon as one of my friends and I started bantering with each other in-character over the quest we had been given, the DM looked kind of horrified.  Once we finished talking, he made some comments like "well, now that that's over, let's get back to the game."

So basically I felt it was immediately obvious my style of gaming was not wanted at this table, and two of the three of us left at the first opportunity.  I imagine the game was better for it, even though I hardly think we were doing anything wrong, nor that a just-mechanics game is inherently bad (though obviously not my thing).

I've left two games early. The last game I left early was in 2014. It was a QAGS game, and there was a player in there who was really dominating the action. To me it seemed like the GM wasn't reigning him in. It's a shame, because I enjoy the QAGS system, and I've had lots of fun playing in their games previously, and I know I had seen the player previously in other QAGS games. I just got tired of it when it seemed like my character wasn't even driving a little bit of the action, so I left.

The other game I left early was a Buffy the Vampire Slayer RPG. This game was a mashup between Buffyverse characters and comic book characters, like Constantine. Two players really started dominating the session, and I finally got to the point where I asked the GM, point blank, if there was any reason for my character to be there. When he said no, I said, ok, my character catches a bus and leaves town. With that, I left the table.

I have no regrets about either time I left the table early. My time is limited, and if I'm not enjoying myself in the game, especially after I've made an effort to bring it up, I have no problem leaving.

A few years ago, I barely escaped a disastrous LARP game.

Everyone had assembled in the room at the beginning of the session, and the organizer said, "Sorry, but I haven't written this one yet. I'll make up some characters for you in a few minutes, and then we'll get started."

I traded my ticket with someone who had generics, and quickly got out of there.
And I'll never attend another LARP run by that group again. Life (and Gen Con) is too short for that kind of nonsense.

This is a bit of a different post.  My group didn't leave but stayed and we probably should have left...

We had a bad experience a couple of years ago with a Vampire RPG game.  It was for people who never played the game and there were 6 total people in the game.   A guy and his wife, 3 people in our group (all guys) and 1 guy by himself.   The GM was very good and the game started out well.  All of us were vampires with different abilities and again nobody has played the game before so we were all flying a bit blind (pun intended).  We came across our first challenge and spent around 10-15 minutes developing a plan, which we all agreed too, and then when we started to implement the plan, the one lady at the table, stopped and went a completely different direction.  She spent 45 minutes of dedicated GM time, just her and him in a near private conversation.  The room was loud and she sat next to the GM so it was like they ran a 1 on 1 game for 45 minutes. Our group of three mentioned this issue about 10 to 15 minutes in to her "side quest", but unfortunately it didn't wrap up.  Everyone else at the table, minus her husband, pulled out cell phones and did other stuff for ~40 minutes.   Now after 45 minutes, we did come back to the original plan and at this point the other players minus this lady's husband wanted her dead.  There were two sides at this table and the poor GM was stuck in the middle.  Knowing it was a one shot made this even worse as I remember saying to the GM who warned me that some action that I was trying may get me perm killed:  I replied  "I really don't care" and him saying something like, "well you will care", and me saying something like "there is really nothing that could happen at this point to make me care about this game".  I felt bad for the GM as he was a cool guy and the adventure would have been great but this lady just consumed 45 minutes of a 2 hour game and didn't move the plot along at all.  At this point for most of the table it was just about doing stupid stuff and way over the top stuff.   The irony is that we were rolling crazy hot, which just added to the chaos and anger of the guy and his wife.    We did finish the campaign with people pissed off at each other and not talking to each other at all when we left.   

Now the irony is that we still remember this game and all the ridiculous things we did and even openly talking about killing this lady's character and family at the table while the game was going on.   Things were so bad at that point that I remember laughing for like 5 minutes as one of our party openly suggested killing this ladies grandmother and we talked about it as she got more and more pissed.  We didn't do it by the way as we could tell the GM was about to just call the game...   

So this was a game that went so bad that we made it one of the most memorable games we have ever played.  I still can't believe how hot we rolled.   One that we will talk about for years to come and one that we learned from.  We now tell GM's when things appear to be getting out of hand and when people are not having fun or a game is way out of balance.   

Lastly, I can imagine people will say that we shouldn't have asked the GM to stop more, but we did try a couple of times.  One at 10-15 min in and another at a half an hour or so.  This lady was crazy demanding and a drama queen.  The GM was a cool guy who didn't know how to handle a lady like that.   

I only ever skipped two events at all the Gen Cons I have been to.

One year there was a Highlander LARP sort of event ran n\by Thunder Castle Games (makers of the Highlander TCG.) I had turned in my ticket, got my packet, but left because I wasn't feeling well. I recall dropping my packet in a trash can. Within the next month, I had hernia surgery. I guess that's why I wasn't feeling well.

Another event I skipped was a boardgame event, one of the Gipf project games. It was a 2 player game, and I had played a related game with a fellow I didn't much care for. He mentioned having the ticket for the other game. I just didn't want to play him again, so I didn't show up. Cannot recall why I didn't like him.

I've only ever had 2 things I left early.

One was a co-op game where the other 4 people knew each other and I was generally left out of any decision making.  Once they started ignoring rules, I just stated 'Sorry guys, you guys know each other so, probably more fun for you if I just cut out'

The other was a 'learn to play' game where the learn to play was (from the "teacher's" mouth), 'read the rules and look at the board and figure it out.' while he sat and ate his supper.   Since I could do that on my own, I walked out (as did half the other players).

Thankfully, that was it over many years of going.