The TOS movie phasers are great, because they took an iconic design and added some more realism. And those "Amok Time" battle axes are just so classic. While we're on the subject of weapons, anything the Klingons come up with is usually pretty neat: that knife with the retractable extra blades, the bat'leth...even their phasers are pretty neat.
On a more peaceful note, I've always been partial to Uhura's ear widget. That may well be the most iconic, and yet mysterious, prop in all of Trek. What does she hear on there? Where does it get its signals from? Is it a remote link to Uhura's comm station, or is the device itself receiving signals from deep space? And most importantly, how long does she have to keep that thing in her ear for? To stay on topic, that right there is probably my favorite Star Trek prop.
And as far as tricorders go, I don't think it gets much classier than TMP's version, although Enterprise's slimmed down hardware is nicely modern.
Honorable mention: Sisko's baseball. Adds a real human touch to the proceedings.