Sorted by actor, Trek character(s), series*, Batman character(s), BTAS episode(s) (unless indicated by BB [Batman Beyond])
*It would take too much time to identify the Star Trek episode of each obscure bit character each celebrity played. So if you can skim through all the color, only the BATMAN episodes are noted where necessary.

Michael Ansara; “Kang” TOS & DS9 “Mr. Freeze” throughout BTAS and Beyond
Rene Auberjonois; “Col. West: ST6, “Odo” DS9 “Dr. March” (“Terror in the Sky”, “On Leather Wings”)
Ed Begley Jr.; “Starling” VOY “Germs” (“Feat of Clay”), “Dr. Peter Corso” (BB “April Moon”)
Adrienne Barbeau; “Creetak” DS9 “Catwoman/Selina Kyle” throughout BTAS
Michael Bell; “Zorn” TNG, “Xelophite Captain” DS9 "Award Presenter" (“Heart of Ice”)
Levar Burton; “LaForge” TNG, VOY and movies “Hayden Sloane” (“The Worry Men”)
Stephen Collins; “Will Decker” ST1 “Tony Mayzhakj/Earth Mover” (BB “Earth Mover”)
Jeffrey Combs; “Brunt” DS9, “Weyoun (clones)” DS9 “The Scarecrow” (“Never Fear”)
Robert Costanzo; “Slade Bender” TNG “Det. Harvey Bullock” throughout BTAS
Olivia d’Abo; “Q/Amanda Rogers” TNG “Ten/Melanie” BB
John de Lancie; “Q” TNG, DS9 & VOY “Eagleton” (“The Mechanic”, “Blind as a Bat”)
Andy Dick; “EMH Mark-II” VOY “Sam” (“The Eggbaby”)
Paul Dooley; “Enabran Tain” DS9 “Father Michael” (“It’s Never Too Late”)
Paddy (Paddi) Edwards; “Anya” TNG “Maggie Page” (“Eternal Youth”)
Michael Ensign; “Krolla” TNG, “Lojal” DS9, “Takarian bard” VOY “Butler” (“The Eggbaby”)
Matt Frewer; “Rasmussen” TNG “Sidney Debris/Sid the Squid” (“The Man Who Killed Batman”)
Teri Garr; “Roberta Lincoln” TOS “Mary McGinnis” BB
Sherman Howard; “Endar” TNG, “Syvar” DS9 “Blight/Derek Powers” BB
Clyde Kusatsu; “Nakamura” TNG “Hill High Coach” and other bit roles BB
Christopher McDonald; “Castillo” TNG “Superman” (BB “The Call”)
Malcolm McDowell; “Soran” ST7 “Arcady Duvall” (“Showdown”)
Michael McKean; “Fear Clown” VOY “50’s Joker” (“Legends of the Dark Knight”), “Ian Peek” (BB “Sneak Peek”)
Kenneth Mars; “Colyus” DS9 “Richard” (“Sideshow”), “M2” (“The Lion & The Unicorn”)
Dick Miller; “Vendor” TNG, “Vin” DS9 “Boxy Bennett” (“Harley’s Holiday”, “Harlequinade”)
Diana Muldaur; “Dr. Miranda Jones” TOS, “Dr. Ann Mulhall” TOS, “Dr. Katherine Pulaski” TNG “Dr. Leslie Thompkins” throughout BTAS
Bill Mumy; “Kellin” DS9 “Warren Lawford/The Fox” (“The Terrible Trio”)
Kate Mulgrew; “Janeway” VOY “Red Claw” (“The Cat & The Claw”, “The Lion & The Unicorn”)
Nichelle Nichols; “Uhura” TOS and movies Thoth Cappera (“Avatar”)
Alan Oppenheimer; “Koroth” TNG, “Keogh” DS9, “Nezu Ambassador” VOY “Auctioneer” (“Time Out of Joint”)
Michael Pataki; “Korax” TOS, “Karnas” TNG “Sewer King” (“The Underdwellers”)
Brock Peters; Cartwright” ST4, ST6, “Joseph Sisko” DS9 "Lucias Fox" BTAS seasons 1 – 2
Lori Petty; “Nos” VOY “Livewire” (“Girl’s Nite Out”)
Robert Picardo; “The Doctor” VOY, DS9 ST8 “Eddie G” (“The Man Who Killed Batman”)
Joe Piscopo; “Comic” TNG “Manager” (“Make ‘Em Laugh”)
John Rhys-Davies; “Da Vinci” VOY “Baron Waclaw Jozek” (“The Cape & Cowl Conspiracy”)
George Takei; “Sulu” TOS, VOY and movies “Mr. Fix” (BB pilot “Rebirth”)
Malachi Throne; “Mendez” TOS, “Pardek” TNG “The Judge” (“Judgment Day”), “Fingers the gorilla” (BB “Speak No Evil”)
David Warner; “St. John Talbot” ST5, “Gorkon” ST6, “Gul Madred” TNG "Ra’s Al Ghul" throughout BTAS and Beyond
Ian Patrick Williams; "Doc Fitzgerald" VOY “Andrews” (BB “Shriek”)
Paul Williams; “Koru” VOY “The Penguin” throughout BTAS
William Windom; “Matt Decker” TOS “Ethan Clark” (“Prophecy of Doom”)
Paul Winfield; “Terrell” ST2, “Dathon” TNG “Earl Cooper” (“The Mechanic”) “D.A. Sam Young” BB

Kurtwood Smith; "Federation President" ST6, "Thrax" DS9, "Annorax" VOY "Agent Bennett" (BB "Countdown")

George Murdock; "God" ST5, "Admiral J.P. Hansen" TNG "Boss Biggs" ("The Forgotten")

Jason Marsden; "Raymond Marr" (voice) (uncredited) TNG, "Grimp" DS9 "Spunky Spencer" ("Baby Doll"), "Donnie Grasso" (BB "Hooked Up") and various other DCAU characters

Dean Stockwell; "Colonel Grat" ENT "Tim Drake" (BB:ROTJ)
Clancy Brown; "Zobral" ENT "Lex Luthor" TNBA, STAS, JL
Mark Rolston; "Lt. Walter Pierce" TNG, "Kuroda" ENT "Garfield Lynns/Firefly" ("Torch Song", "Legends of the Dark Knight"), "Carl" (BB "The Eggbaby")

Angie Harmon ADA Brunette Barbie III, Law and Order Comissioner Barbara Gorden, Return of the Joker.

Yes. But was she in Star Trek? (see topic title)

Jeffrey Combs; "Weyoone" DS9, "Brunt DS9, "Shran" ENT The Question, Justice League Unlimited

I don't see a topic specific to the Adam West TV series, but of course, those of us who cherished it remember the bat-climb cameos. Thinking of Werner Klemperer's in-character appearance caused me to think about a Lost in Space cameo:

(Batman and Robin paused as the window opened and Jonathan Harris leaned out.)
“What manner of entering this building are you two so audaciously engaged in?!”
“Dr. Smith!” Robin exclaimed. “I thought you were lost in…”
“That’s what you thought, Boy Blunder!”
“As a duly deputized officer of the law,” Batman remarked, “I should take you into custody on suspicion of espionage. However…”
“However?” Robin and Smith both inquired.
“We are presently attempting to apprehend an arch-criminal, which should assume a higher priority…”
“An arch-criminal? A higher priority?!” Smith bellowed. “Indeed! I should think I was worthy of such a priority! I would prefer to take insults from that bubble-headed booby back on the Jupiter II!”
“Well, give my regards to the family,” Robin said. “I hope you folks find your way back here someday.”
“I rather doubt it,” Smith said with contempt. “Without my genius and tremendous labour contributions, they wouldn’t find their way out of a Batcave!”
He closed the window and the Dynamic Duo continued their Bat-climb.