Sooooooo many good moments its hard to choose just one. So I'll go by individual games.
WC1: The whole game was amazing from a design perspective, it really drew you into the game. The briefings felt directed at you, the debriefings added weight to your actions, the dogfighting with aces felt really personal, the talking heads in the Bar between missions were all full of personality. And who can forget the promotions and medals? Finally earning a Pewter Planet without cheating was a crowning moment on a game that is one big excellent moment.
WC2: The story really picked up here (Blair being considered a traitor, Spirit's death, Jazz, Hobbes, Angel, etc.), Broadsword jumping/refueling, Torpedo Runs, blowing up Ayer's Rock in SO2.
Privateer: Of all the things this game did excellently: running away from superior numbers and jumping out right before they can slag you was perhaps the best moment the game offered.
WC3: The tension between Tolwyn and Blair, the Behemoth, Hobbes betrayl, the final fight with Thrakkath and the trench run on Kilrah.
WC4: Blair et al. seeing the effect of the Gen-select bioweapon, and the final confrontation at the Senete.
Privateer 2: Learning that Clive Owen is the true heir to the largest crime syndicate in the Tri-system...and then being disappointed when you can't exploit that in-game in any fashion (seriously shouldn't you get a Kindrid base, or for them to at least stop attacking you). Really this game needed some kind of sequel or expansion.
WCP: Learning that the Nephilum were not as easy to shoot down as Kilrathi....*sigh* The final confrontation at the worm-hole also had a nice epic feel to it.