I was just browsing through internet today and got curious to know the age of any website. I googled it but could not find any satisfactory answer.

Then, i decided to use some common sense and found these tricks useful to approximately know the age of a website. You may also find them useful and in case you have a better way of figuring this out, please share it in comments.
There are two types of dates associated with a website:

1. Domain name registration date: Domain name is nothing but the name of the website. This is the date when the website owners would have registered it on internet.
   This date can be easily found using the Who is database. Just visit this website, enter the domain name and click search. if the domain name is already taken, a new button will be shown against it with name 'who-is'. Click this button and they might ask you to enter some security image characters just to make sure that you are human!!).
   
   Once you are through, the data will show you the domain registration date, expiring date, time duration for which the domain has been registered etc.. The contact details of the domain registrar and owner are also available including their email-id in case they have not opted for private registration. Private registration is done to avoid disclosing the owner details
   
   
   
   So, looking at this data, you can easily apporimate the age of the website. Obviously the owners would have registered and then only it would have appeared on internet!!
2. Date on which the web page first appeared on Google: Well, this date cannot be 100% accurate to estimate the age of a web page (note i am talking about web page and not web site), but can give a fair bit of idea about when it was tracked and indexed by Google. Also, remember that not all web pages from a web site are indexed by Google.
   
   Go to http://google.com and type the following in search box:
   inurl:http://YOUR-WEBSITE-NAME
   Example: inurl:http://am22tech.com
   
   
   
   Now, you can see a an option called 'Show Search tools' in left hand pane. Click it to expand the search options.
   Click on 'Custom range' under 'Any time' and select a time frame of around 10 years. If you feel that the website you are looking for might be older than that, you can very well increase the time frame.
   Now, clicking on search will find the web pages with the given website name with their first Google indexing date i.e. the date when google had first read that page. If you look at the example picture above, the very first google search result page from our website appeared on Google on 23 Aug, 2010.
   
   Please note: This does not mean that the website was started on 23 August, 2010. This date is only relevant for that particular web page and not the whole website.

The above two options can certainly give you a fair bit of an idea about the age of a website, if not the exact one!