A lot depends on context. What issue or subject is being discussed? Does the fallacy appear to be unintentional?
Keep in mind that there's a HUGE difference between the scientific/philosophical arena and the political arena. In the former, we engage in discussions with peers, colleagues or (in philosophy) interlocutors. In the political arena, we're generally talking about verbal combat.
If two or more sincere people are attempting to conduct a rational discussion, then they should be mature enough to consider all the arguments. In this spirit, if one person engages in a fallacy, I would suggest tactfully pointing out that fallacy, at the same time noting that it may have been unintentional.
You wouldn't even necessarily have to label it a "fallacy;" you could simply describe it as an illogical statement.
I would expect a group of scientists or philosophers to have a mature discussion, pointing out flaws in each other's arguments without engaging in suits. In theory, such a discussion could and should be possible in the political arena as well.
Unfortunately, politics is what it is - and it often intrudes in the scientific and philosophical arenas as well.
I generally steer clear of political discussions unless I know the person I'm talking to is sincere (e.g. honest) and relatively intelligent. But if I do find myself in a conversation that someone is deliberately trying to sabotage with fallacies, I won't hesitate to call them out.
As noted in the other answer, this might provoke your opponent into retaliating, pointing out YOUR fallacies. This is the moment of truth.
If you've been making an honest effort to discuss a topic in a rational manner, you should not have committed any fallacies. Yet it's possible to introduce faulty logic into a discussion without realizing it.
So now you have to think fast. If you've been exposed, should you admit that you committed a fallacy yourself? If so, should you elaborate or claim that it neither intentional nor as serious as your opponent's fallacy? (Notice I used the word "opponent" rather than "interlocutor.")
And will you even have time to make such an argument? Will the audience understand all your comments and arguments regarding fallacies?
As Frank Hubeny pointed out, you could wind up distracting attention from the primary topic.
Going back to square one, I'd be very careful about getting involved in a conversation with a person I don't know and respect. And if there's an audience, that suggests a public forum or media event, both of which are shamelessly rigged. Generally speaking, you'd be a fool to get roped into such a discussion.
But if I did get involved in that kind of discussion, and my opponent was trashing my logic with fallacies, I'd consider that a declaration of war, and I'd fire back.