Bad form, and quite rude.

EDIT: Cirmustanses both ways, but usually it's bad. Usually there are other people waiting to play the machine etc etc. Maybe if there's time, and it's the end of your match it might be ok. If it's liek the first or 3 games that's a huge no no. Rookie move.

If I'm player one, and player two is having a great game, I'll tell him to play his last ball through (if he wants to).
There may also be cases where scoring is used to determine tie-breakers, but that's fairly rare.

If it's a game you are not really comfortable with and you think you may play it again later in the tournament play your ball. If it's a game that you are comfortable on just plunge it. Playing the 3rd ball in that situation should only be played if you are trying to learn the game or get more comfortable with it. If someone get's upset because I played the 3rd ball for that reason that's their problem.

Edit - I'll add that it would be polite to at least advise the other player what you are doing. For instance I'll normally say, "you mind if I play this last ball a bit? I'm not real familiar with the game and would like to learn more about it.? I've found two things happen at that point. One, is the other player has never said "no" (if they do I'll play it anyway) and after the game the other player has almost always given me tips for the game to help me learn. Doubt you see this much in "A" division's as most know all the games but seems to be a non-issue in the lower groups.

Like Josh Sharpe has said " Act like you've been there before".

Now, in our league scoring, the last ball is often played because there are bonus points up for grabs. Example, player three's score is greater than the sum of player 1 and 2 score, then player 3 gets a bonus point.

That's a good point

I don't do it, but I don't care if other people do. I would consider it if it was truly an epic game on the cusp of reaching something I hadn't seen before - but only if it wasn't holding anything up. I'd "ask" permission of my opponent too.

That's about the only good reason. And as mentioned, you should explain why you are playing it to the other player and anyone else watching. Going for a personal best score, GC score or loop champion are not good reasons to keep playing. That's disrespectful.

The unflipped third ball is a rare treat in pinball. You've vaquished your opponent with only two balls. I very much enjoy doing it on the rare occasion it happens. It baffles me when non-rookie guys keep playing.

I'm not as calcualted as others regarding score so I may go over the score a bit till i get a break in the action. Although most people that know me just yell at me to stop.

The majority of the time, I just plunge it. If I am having a killer game and there isn't anyone waiting on me, I'll play it. Case in point was my TOTAN game during our monthly tournament two months ago. I had player one beat on ball 2, but I was killing it and everyone wanted to see me finish it out. Ended up battling the genie twice and over 100 million without any extra balls. It did get a little long though, so I kinda stopped trying and let it drain when it didn't have to. 9.5 times out of 10 it doesn't matter to me, but in this case though it was fun to play it out.