I know only about Shadow King and Professor X were there .

Adam Warlock of course, Dr. Strange and so on

Didn't Storm and Ainet also go to the astral plane?

I almost went but I forgot my passport.

Sinister and Moondragon

Illyana Rasputin used her magic to enter the Astral Plane to locate Kitty Pryde, back when the New Mutants went to the Massachusetts Academy to rescue her and confronted the Hellions for the first time. 
 
Dani Moonstar accompanied Professor Xavier onto the Astral Plane when they telepathically entered Legion's mind. 
 
Karma has battled the Shadow King on the Astral Plane.  
 
Gamesmaster held 'conference calls' with the Upstarts on the Astral Plane, much like the staff at the Xavier Institute used to have meetings there so they couldn't be over-heard.
 
Of course, there're other telepaths like Jean Grey, Psylocke & Emma Frost although I can't recall specific instances.

Captain Atom has been there three times. Swamp Thing sent him there the first time. The second time required Red Tornado's essence to fill Atom's lungs. The third time, Captain Atom meditated (and probably used the Quantum Field at the same time) to teleport there.

The Silver Surfer. The Power Cosmic is based in the astral plane and there the Surfer cannot be harmed. 
 
Although two were named above, Thanos, Professor X and Adam Warlock also fought the Goddess on the astral plane. (unmentioned characters in bold).