Crystal is number 1 and then cunard lines.They are the very best. Conde Naste magazine has named them 1 and 2 for a very long time. But Princess, Royal Caribbean, and celebrity all treat you like a king or queen and are more affordable.
References :

The worldds higest rated ship at 5 and a half stars is Hapag Loylld’s Europa at 5+. However she is predominently a german ship which does some english sailings.

Here is a list of the worlds 5 star ‘luxury’ ships in order of how well they scored:

SeaDream I
SeaDream II (both SeaDream Yacht Club)
Seabourn Legend
Seabourn Pride
Seabourn Spirit ( http://www.seabourn.com )
Silver Shadow
Silver Whisper (www.silversea.com)
Hanseatic (hapag loyd)
Silver Cloud
Silver Wind
Queen Mary 2 (3 class transatlantic liner only grill class (or first class) is 5 stars,
Sea Cloud II
Sea Cloud
Crystal Serenity
Crystal Symphony (crystal cruises)
Seven Seas Mariner
Seven WSeas Voyager (Regent Seven Seas)
References :

A luxuty cruise is considered to be a cruise on one of the luxury cruise lines.

Crystal Cruises http://www.crystalcruises.com/
Cunard Line http://www.cunard.co.uk/
Regent Seven Seas http://www.rssc.com/
Seabourn Cruise Line http://www.seabourn.com/
SeaDream Yacht Club http://www.seadreamyachtclub.com/
Silversea Cruises http://www.silversea.com/
Windstar Cruises http://www.windstarcruises.com/cruises-home.asp

Seadream Yacht Club is considered to be the most luxurious cruise line and has consistently won awards for being the best.

"Exclusive" above Luxury – Berlitz Ocean Cruising and Cruise Ships 2008
"World's Best" Travel + Leisure 2007
"World's Best" Top Scoring Cruise Line - Condé Nast Gold List 2007
"World's Best Small Passenger Shipping Line" - Condé Nast Traveler Reader's 2006
References :

Cunard - without doubt
References :
Regular Cunarder