Yes, Wing Commander was brilliant. I haven't managed to find a worthy successor to it either, but there are a few contenders, most of which have been mentioned here.
It's worth pointing out that the X series of games (e.g. X - Beyond the Frontier) are very much biased towards the trading aspect of space travel, so they're much closer to Privateer than the 'main' branch of Wing Commander. They are also rather lacking in storyline, although there is a half-arsed one there if you can be bothered. I personally found them rather tedious, due to the amount of flying through empty space you're forced to endure, punctuated by lame battles that aren't much fun either.
Another game worth a mention is the Battlestar Galactica game that was released on the Xbox a few years ago. I don't have much experience with it, but for the short time I grabbed the controls, the gameplay felt very much like Wing Commander Prophecy.
If you're not averse to a bit of fan-produced fun, there are a couple of surprisingly competent Wing Commander fan games out there:
Unknown Enemy and
Standoff. These games both utilise the 3D engine from Wing Commander Secret Ops - the freebie companion to Prophecy - and add their own fiction and game assets to form new episodic adventures. Unknown Enemy has you fighting for the Union of Border Worlds, while Standoff is some kind of re-imagining of Wing Commander 2 - can't rememember the details. They're both great fun and have a very nostalgic air about them, as they both revisit capital ships from the older games and utilise the older, pre-Prophecy style of dramatic music.
I would recommend Unknown Enemy first and foremost, as it's the best fan game I've ever played. Not that I've played much of that rubbish...
