Chaotic neutral characters can be described as the ultimate free spirit. They aren’t bound by any sense of law and they couldn’t really care one way or the other about the fight between good and evil.
This is another alignment where personal gain seems to be the primary motivator. In one instance they can be acting for the greater good, but they would just as soon turn on you if it seemed like it could be to their benefit to do so.
Chaotic neutral characters in general can’t stand self-righteousness and are generally in favor of letting people do what they wish barring extreme circumstances. Still, they aren’t completely callous and do generally have some redeeming features that prevent them from being outright evil.
Think Captain Jack Sparrow from the Pirates of the Caribbean movies. He’s almost a quintessential example of this alignment at work. This is especially the case in the first movie where you were never really sure where his loyalties lay because he kept jumping back and forth whenever he saw an opportunity for himself.
Selina Kyle, better known as Catwoman, is also a pretty good example as she breaks the law, but also helps Batman in his fight against other Rogues Gallery members on a fairly regular basis.
This is another alignment that lends itself to recurring NPC characters, but players can take the alignment and make it work as well.
The alignment grants the player a lot of freedom, but despite this, many people aren’t fans of the alignment. It basically allows the player to do whatever they want without needing to worry about morality or consequences, which somewhat defeats the purpose of having alignments in the first place.
A lot of players also use it as a loophole in order to do things that would qualify as “evil” without officially being designated as such. This can become especially frustrating for DM’s who don’t allow evil characters to be used in their campaigns. It becomes even more frustrating as the DM can’t argue anything because the bipolarity is part of the alignment’s nature.
The flexibility to do whatever you want can be appealing to some players, especially ones who aren’t fond of the concept of the alignment system in general, but you do have to be careful when playing this as it can lead to frustration from other players. Frustration or not, it has a place in the overall spectrum as there are some people who act in this fashion.