It strongly depends on the GM and the general RP rules. There are some RPs that call for strict moderation, specifically when the GM has a specific storyline in mind, or something like that. Of course, some individual autonomy has to be allowed in almost every case, otherwise you're probably going to have some pissy players. Some GM's (like myself) prefer a laissez-fare style of GMing, where players are fairly autonomous, though usually in these cases the GM would step in if something gamebreaking occurs. For instance, in my STALKER RP, one of the characters shot his employer in each of his limbs because his character is an extremely bloodthirsty SOB and he wasn't happy with the NPC's guards shooting at him. I had to ask him to change it because it went too far, and he did so graciously. It's the only time I've had to interject, so far.

There are other RPs where players have a large amount of autonomy in what happens with the storyline. If I recall correctly, Apocalyptica is a lot like that, where each character has their own story and they write it as they go with relatively little moderation from the GM (aside from basic shit, of course).

For the most part, it just depends on the GM and the RP in question. Every RP is done differently and with different levels of moderation.