Specialist Domain WHOIS

Webhosting.info
Regular WHOIS & IP lookup and a free "reverse IP" service (this shows which other sites are stored on a server). 

Domaintools
Free for WHOIS, but paying subscribers can also list other sites on a server and check historical domain registration info.

Dialog
Uniquely allows you to  find past & present domains registered by a named individual.  Free, but full reports are charged for.

See also  
Allwhois.com - for international domains Whois.net - for expired domains & search.
DNS STUFF - brilliant for difficult to find domains

Specialist IP address WHOIS

Visual Traceroute 
Geographically trace the actual server containing a Web page or allocated an IP address. 

Netcraft report
search for a domain by keyword, click site report for WHOIS, then "netblock owner" for other sites on the same IP address block!

Search by IP
Interrogate a search engine's database for other sites on the IP address of a site.

Coolwhois
Whois a domain, find its host's IP and WHOIS that as well!
DNS Stuff
Various tools to probe a server. 

WHOIS from the source - the Internet Authorities

International Domains
Find which body oversees domain name registration for a country - great for finding obscure WHOIS.

Generic Domains
Authorities for domains that don't have a country code or US generic domains.

See also
Nominet - who oversee .uk domain names
IANA - for .int international domains
The TV Corp. - WHOIS for the .tv domain
DotFM - WHOIS for the .fm domain
anything else - try Netsol

International IPs
Find which regional authority handles IP address allocation for a country. 

RIPE
The IP issuing authority for Europe, have the best WHOIS lookup for European IP addresses.

See also
ARIN for Nth America 
LACNIC for Latin America & the Caribbean
APNIC for the Asia Pacific region
AFRINIC for Africa