Can I detect what webserver a website is using?

You can use Netcraft What's That Site Running for a one off query.

You can use

wget --save-headers superuser.com

Which will dump the server headers into a new file index.html which you can then view in a text editor.

Eg, for this site:

HTTP/1.1 200 OK
Cache-Control: private
Content-Type: text/html; charset=utf-8
Expires: Tue, 16 Mar 2010 22:54:59 GMT
Server: Microsoft-IIS/7.5
Date: Tue, 16 Mar 2010 22:54:58 GMT
Connection: keep-alive
Content-Length: 119466

If you need a one-liner to just report the webserver type only and filter out the unwanted stuff then use:

wget -q -O- --save-headers superuser.com | grep '^[Ss]erver:' | awk '{print $2}'

raw:

curl -I duckduckgo.com

filtered:

curl -s -I duckduckgo.com|grep Server

or

curl -s -I duckduckgo.com|sed -n '/^Server:/p'

or übercool

curl -s -I duckduckgo.com|awk '$1~/Server:/ {print $2}'

or for poser

curl -s -I duckduckgo.com|sed -n 's/^S[erv]*: //p'

only for unixoide OS!!!

For a public website, you can use Netcraft - http://netcraft.com/. It allows you to plug in a website's address, and it will analyze the headers and tell you the webserver in use.