The Webby Awards :
The website you create can be honored here with an entrance fee. Websites is but one of four categories to choose from as an award and an entry can be listed in more than one category. This award is overseen by the International Academy of the Digital Arts and Sciences. There is a grand award ceremony for the winner with statuettes as prizes as well as mention in the winner's gallery online and icons to post on the site.
The Best Designs :
This is an award offered throughout the international community with recognition given as mentioned on their website that is reported to have over a million hits a month as therefore would be a great promotional tool for the websites you create. There are several stages before you get to the final few that are considered for the Best Design.
American Design Awards:
This is one of the more recognizable awards to receive when it comes to website creation. It was founded by graphic designers and offered as a platform from which others can showcase their talents in an ethical fashion and in a way that offers good business sense. There are monthly contests as well as semi-annual contests. This doesn't cost anything to enter and is graded on creativity, effectiveness, practicality and ethics. A website cannot be more than five years old.
These are just three of the most visited website design awards that are available to the creative to show off their work. Find your niche and go for the gusto!