Is it a copyright violation...

to have video game characters appear in your sites banner without having asked permission for it from the publisher?

For example on gonintendo.com 's banner there appears mario and various other characters. Did they get permission for that? Do you need permission for well known characters to appear in your web design?

 

i would say yes it is a violation because that character is most likely trademarked.

 

No, it is not a copyright violation unless if you are profiting off of the appearance. It is considered fair use.

 

Is it considered fair use if I do profit off the adsense on my site while having such video game image in my banner or logo for example?

 

It may or may not be a copyright violation, but it is highly likely to be a trademark violation. The question is would the copyright/trademark owners take issue with the way you are using their copyrights/trademarks.

Also, don't automatically assume your usage would fall under fair use rules. There are very steep requirements to fall under fair use. It takes much more than just not profiting off of the usage to meet fair use requirements.