This is not meant to be about any main characters. I'm going to play OPs Privelage for One of mine (which will become clear why) but otherwise, let's keep it fun and to those unsung heros...

1. Lieutenant Hawk.
OP's Privelage here, as he had more lines than most background/supporting characters... Thanks to the performance of Neal McDonnough, this guy was fantastic. He perfectly integrated himself in every scene he was in. Never once scene stealing from the established characters or actors, but always doing a little 'something' to be part of the action, whether it was the subtle head turn in the opening bridge scenes, or the looks he gave to Picard and Lily while suiting up for the space walk. This was a character who could easily have become a Full Time resident, and perfectly fitted into the existing dynamic. He deserved a better end than to be partially assimilated and put out his misery by Worf... RIP Lieutenant...

2. T'Pau.
Why? The woman was a legend! When she was presiding over Spock's wedding, it was like being at court with Queen Victoria. One wrong word, and you knew you'd have your ass handed to you... So when they showed her as a young woman in Ent, and what she was like then, that was fantastic.

3. Kell Perim.
Wow. Definitely more going on behind those eyes than most Bridge Bunnies. She may have looked like a librarian/school ma'am, but I bet she was all 50 Shades off duty

4. Jae.
She was awesome. Sometimes at the helm, sometimes at a science console, always present, but never drawing attention to herself, the perfect extra...

[Edit to add name to Number 4 ]

1. Ensign Riley-TOS. Loved his remark "He died, because he wasn't born an Irishman."Then, his borderline drunken singing over the com that drove the bridge crew nuts.

2.Blonde female helmsmen who replaced Wesley for a few episodes.She was just eye candy, but a competent officer.

I'm sure I will think of more,but thats all I have at the moment.

Morn. Always had a story to tell, brought humility, humour and a raw emotion to every scene he graced. Plus he was the hero of the dominion war by getting the message out to the Feds about the minefield.

The guy was the linchpin of the entire franchise. Take him out and the entire thing unravels.

Definitely Jae from TNG. She looked like a strong and confidant officer, and for some reason I loved her hair.

Abdullah bin al Hussein, the King of Jordan. He did a cameo (he was a prince at the time) as an "Unnamed Human science officer" in the opening scene of Voyager's episode "Investigations". (http://en.memory-alpha.org/wiki/Abdullah_bin_al-Hussein)

Currently he is majorly invested in the Star Trek theme park being built in Aqaba, due to open in 2014.

Yes! That's her! Awesome to finally put a name to the face

I wouldn't go so far as to call him the linchpin, that title would likely go to Sisko, Kira or Dax (the character, not either specific actress), but DS9 would have been radically different without Morn. And he did it all without saying a single word.

From purely an acting angle, the crown has to go to one Mr. Jeffrey Combs (Shran/Weyoun/Brunt). The only people I've ever seen get more into an alien role were Peter Jurasik and Andreas Katsulas in B5 (if you haven't seen Londo and G'Kar go at it, you need to. The chemistry that pair had is something I've never seen the likes of in any other show, ever).

*Bump*
To hear more of folks thoughts

Morn. Do I really need to explain why? Everybody loves Morn!

TOS: Mister Leslie, the only redshirt known to have died and come back to life. Or, he had a twin brother who coincidentally served on the same ship.

TNG: Lieutenant Hawk for all the reasons the OP stated. Also Kell Perim.

But I'd also like to mention Ensign Sito Jaxa. What an incredible character, what a great arc, what a lovely young woman, what a tragic end.

DS9: Enrique Muniz. Great guy and sadly missed.

Voyager: Kaidan Alenko. /jk