In the Enterprise episode "Fortunate Son", which takes place around the year 2151, it is mentioned that the Nausicaans are mainly pirates:
ARCHER: Sorry we couldn't meet under better circumstances. What happened here?
RYAN: Nausicaans. They tried to board us. We managed to fight them off but not before we took a few bruises.
TRAVIS: Pirates, sir. They've been attacking freighters in this sector for years. My parents had a run-in with them once. They were lucky to come out of it alive.
According to an early version of the script, they also seem to have some sort of government, albeit an unstable one (thanks to Valorum for pointing that out):
In the first draft script of "Fortunate Son", the Nausicaans were referred to as indeed having a government on their homeworld. However, it was said that, according to the Vulcans, this government was in a constant mode of "transition".
In the DS9 episode "Bar Association", it was shown that they are also well known for being thugs, guns for hire and body guards:
BRUNT: That's Liquidator Brunt to you. I see you remember me.
(Brunt is accompanied by two Nausicaans.)
and later on:
QUARK: There's plenty to talk about. The FCA's involved now, and those Nausicaans working for Brunt aren't just for show.
QUARK: It's nothing to smile about. Those Nausicaans shattered my left eye socket, broke two of my ascending ribs and punctured my lower lung. If Odo hadn't come along when he did.
According to Star Trek Online, which is debatable how canon it is, by 2389 there seems that there is some sort of government:
In 2389 the Gorn Hegemony hires the Nausicaan government to support them in their conflict with the Klingon Empire.