Personally the old and hard to find spaceship dogfighting game has two of my favorite mechanics.
First for hitting each weapon has a combination of dice that are rolled against a Defensive Value. For example a basic Pulse Laser hits at 2D8+Gunnery (where Gunnery is D4, D6, D8, etc.) However the coolness of the mechanic comes in because the Damage is just Low, Medium, High. So if you rolled a Pulse Laser with a ho-hum pilot (2D8+D6) and got a 4, 7, and 8 the damage would be 4. I really like not having the second roll, and how it still has great variety between weapons. They obviously account for multiple Lows (like if you roll 4, 4, 7 you'd just add the two 4s together) so there is sort of a critical hit mechanism going on there.
So that's all neato, but my favorite mechanic is still their damage track. I've played games of Battletech and the like where you slowly fill in dots to represent armor damage, and that's all well and good, but the damage track is Silent Death is awesome because it actually degrades the performance of the ship. Basically it's a grid (say 10 rows long and 4 rows high) with different items in some of the grid points, like -1 Drive, -1 Defensive Value, Weapon Lost, etc. Then when you take damage (like 4 damage) you would mark off 4 boxes and apply any effects that were marked off. So as you take damage your speed is reduced, your armor is stripped away, you start losing weapons, etc. until your ship is either dead in the water or actually destroyed.
I don't know how well I described it but the elegant degrading and simple hit/damage mechanisms are amongst my favorite mechanics.
In general though I'm not a fan of D6 based mechanics...I'm kind of bored of the dice and the limited granularity it provides. D12 is my current favorite, but that might be from too much Advanced Heroquest as a kid.
And in case we were going to get into least favorites I'd have to put in my vote for Warhammer 40,000. My friends are enamored with the game and I hate playing it compared to the many, many stellar alternatives. But the fact that you have to do 7-BS=what I need to roll to hit, then roll a ton of D6s, then roll to wound (checking a chart to compare Strength and Toughness) and then roll saving throws just for shooting is hilarious awful.