Gotham City has quite a few interesting villains. There's always been the question of whether or not the costumed villains are there because of Batman. Batman's rogues gallery has a diverse mix of bad guys, most with some sort of gimmick or theme. It's because of these gimmicks that when caught, they are usually sent to Arkham Asylum, an asylum for the criminally insane.
Villains rarely set out to accomplish their mad schemes alone. They are known to have a gathering of thugs or henchmen at their side. The question of where henchmen come from was brought up before. What happens to them after they are caught?
In the different depictions of Arkham Asylum over the years, it's a pretty big place. Even if you took all of Batman's villains, there'd still be enough room for other inmates. Not all of Batman's villains are considered insane, even if they choose to wear a costume and base their crimes on a specific theme.
There is also Blackgate Penitentiary located in Gotham Bay. Blackgate is where other criminals go. Past inmates included Bane, Catwoman and Cluemaster. There seems to be some discrepancy as to where Batman's villains belong. I brought up the question of whether or not Mr. Freeze belongs in Arkham. He has been portrayed as being obsessed with trying to save his wife Nora but originally he was a simple crook forced to where an air-conditioned suit. He never really seemed to be insane. Batman has even said that the inmates of Blackgate are as dangerous as the ones in Arkham since they are "not crippled by dementia."
While there is the question to where some of the villains belong, the same goes for the henchmen. They are just hired thugs. They choose to follow the villains' orders in the hopes of making a name for themselves and earning some big money. What does that say about their mental state?
It could be argued that they are just motivated by money and not necessarily crazy. Getting a gig with Joker could or Penguin could lead to some big scores. If henchmen kept resumes, being able to say you worked with some of the biggest names in the criminal underworld would carry a lot of weight. It could even lead to the thug getting their own little criminal empire if they earn a big enough reputation and learn from their experiences.
On the other hand, you almost would have to be a little insane to choose to work for someone like Joker or Penguin. There most likely isn't any health benefits offered and they have been known to kill the hired help when part of a scheme goes wrong. Working for a costume villain pretty much always ends up with the 'boss' being defeated by Batman and getting sent to Arkham. Do the henchmen really think the next plan will be successful? A rational person would know better than to hook up with a boss that is known to be insane and a killer.
Not only is Gotham City under the protection of Batman, but his countless allies as well. Small time criminals might be able to avoid his attention for a while but the 'costumed crazies' are almost guaranteed to attract his wrath. Willingly risking your life to work for an insane killer in a bright colored costume with the guarantee to get busted by Batman doesn't instill too much confidence in a thug's sanity. Arkham is usually reserved for the big time disturbed villains but we have seen other petty inmates inside as well.
They may not be on the same level of crazy as the big villains but you have to wonder what they must be thinking to join forces with them. But they most likely wouldn't be at the same level of insanity as the other inmates of Arkham. For the henchmen trying to decide where to seek employment, they might want to consider the fact that working for an insane villain could lead others to believe they are insane as well. That could make a huge difference when it comes time to being incarcerated. Henchmen don't want to get locked up but being locked up with the criminally insane could lead to a different level of dangers than in a regular prison.