The most important one is the Webby Awards - but you already know that.

There are several other important ones, such as the Advertising Competition and the ISPA Awards.

http://www.advertisingcompetition.org/
http://www.ispaawards.org.uk/
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The most important internet/interactive awards that I am aware off are the webby awards. To the Internet world the webby awards are the equivalent of the movies oscars awards.The deadline is December 19th according to their website.It has over seventy categories and it will be their 12th annual award ceremony,the first having been held in 1997.It's been dubbed by the NY times as the "internet's highest honour".I Hope that helps.
Source(s):
http://www.webbyawards.com/
http://en.wikipedia.org/wiki/Webby_Awards

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Although it is fairly new, I like the Mashable Open Web Awards.

"Open Web Awards is the only multilingual international online voting competition that covers major innovations in web technology. Through an online nominating and voting process, the Open Web Awards recognizes and honors the top achievements in 26 categories."

The dates are early Nov. through Dec.
These were the 2008 dates:
* Wednesday, November 5th, 2008 | Nominations
* Wednesday, November 19th, 2008 | Online Voting Round 1
* Wednesday, December 3rd, 2008 | Final Round Voting
* Tuesday, December 16th, 2008 | Winners Announced
Source(s):
http://mashable.com/openwebawards/home/

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It depends on whether you are looking for regional or worldwide awards. For instance, the UK Internet Industry Awards took place in March of this year, where web host UKFast won their ISPA award for the fourth time. The 2009 awards will be held in July of 2009 in London. Other awards include the IEEE Awards which are sponsored by Nokia.
Source(s):
http://www.ispaawards.org.uk/
http://www.ieee.org/portal/pages/about/awards/medallist.html

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