Recommendations
Basic Starting In you have no idea what to get, any of the following would be a good start  
Blow The Man Down A Collection: Louis Killen, Ewan Mac Coll, AL Lloyd, Cyril Tawney etc.  
Sea Shanties and Sailor Songs The Shanty Crew This CE from England has 29 good recordings, It also has 50 page book that has all the words and an explanation of each song
Songs of the Tall Ships The Starboard List a CD with 30 tracks covering all the well known Chanteys
Sailors Ships & Chanteys Louis Killen  
Deepwater Shanties Holdstock & Mac Leod  
Good Listening    
Hearts of Gold Pint & Dale  
Huaaz Old Ironsides Geoff Kaufman  
Irish Ballads & Songs of the Sea Dan Milner  
Whaling Recordings dealing mostly about the whaling industry  
Leviathan AL Lloyd  
Soundings for the Whale (Tape Only) The Morgans  
Whaling and Sailing Songs Paul Clayton  
Modern    
Tinker Taylor Soldier Singer Tom Lewis  
at South Street (Tape Only) Spindirft  
Hove to and Drifting Bob Zentz  
Trawlertown John Conolly, Pete Sumner  
Historic Recording that are as close to what was originally song on ship (slow, energetic, little if any harmony)  
From Salthouse Dock Bob Webb  
My Ship Shall Sail the Ocean Compilation Traditional Music of England, Ireland, Scotland and Wales. A real collection of old recording dug up from Topic Records archives, some live performances, and field recordings
Other ones I Like    
a Hundred Years Ago Warp Four  
Crossin' the Line Ancient Mariners Chantey A series of chanteys laid out to form a story of the sailing of the Connecticut complete with sound effects and narrations
Tape La Galoche Mes Souliers sont Rouges  
The Canaller's Songbook Golden Eagle String Band