Okay, just because nobody else has done it yet:The following are all ships listed or mentioned by name (or at least, all I could find) in LUG's ST:TNG roleplaying game handbooks "The Price of Freedom" and "A Fragile Peace," as well as the core game book. (I don't have any other books yet, although I know the Intelligence Handbook and "The Way of Kolinahr" are out. They're on order.)
This list will include some canon ships, so don't go making new entries beside ones you already have.
AKIRA CLASS:
Akira
Black Elk
Nez Perce
Susquehanna
Geronimo
Mateo
Thunderchild
APOLLO CLASS:
Apollo
Agamemnon
Ajax
Clement
Gage
T'pau
Chronos
McHenry
CONSTELLATION CLASS:
Constellation
Gettysburg
Hathaway
Magellan
Stargazer
Victory
Antietam
Fading Sun
Vespucci
DENEVA CLASS:
Deneva
Arcos
LaSalle
Eridani
Indi
MERCED CLASS:
Merced
Trieste
Calypso
Pumari
MIRANDA CLASS:
Miranda
Vigilant
Andover
Brisbane
Mondial
NEW ORLEANS CLASS:
New Orleans
Kyushu
Renegade
Rutledge
Santa Fe
Thomas Paine
Herbert
Jefferson
Savannah
NIAGRA CLASS:
Niagra
Princeton
Raleigh
Thims
Wellington
Wells
Fairfax
Joshua Tree
T'Pavis
NORWAY CLASS (some discrepancy with Sabre, here, probably typo error)
Norway
Denmark
Prague
Arian
Luxembourg
Triumph
OLYMPIC CLASS:
Olympic
Biko
Hope
Noble (Nobel?)
Pasteur
Peace
Hippocrota
Mayo
Moore
Tranquility
RIGEL CLASS:
Rigel
Akagi
Arcturus
Barnard
Sirius
Tolstoy
Deneb
Polaris
Vega
SABRE/SABER CLASS: (some conflict with Norway Class)
Sabre
Denmark
Shepard
Yeager
Arian
Luxembourg
Triumph
STEAMRUNNER CLASS:
Steamrunner
Great Smokey
Matewan
Sutter
Shenandoah
Wanderer
others:
Sovreign - Sovreign Class - NCC 17454 (WAY too low, typo again?)
Temple
Tat'sahr
Mizar
Lor'vela
Fearless
Nakashima
Discovery - Nebula Class
Beowulf
Manassas - Ambassador Class
Anduril
Ward
Himori - Nebula Class
Montgomery - Oberth Class (HEY MONTY!)
Ticonderoga
Fortunate
Genevieve - Freighter
Apollyon - Freighter
D'vairin - Romulan warbird
Sha'arik - see above
Kamerain - Orion merchant/cargo ship
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You're just JEALOUS because the little voices talk to ME!