1. TIE Fighter Collector's CD-ROM 1995 Edition
This is my favourite game ever made, so obviously it is my favourite Star Wars game too. You can buy TIE Fighter from GOG.com and it will come with the Collector's CD-ROM edition included - make sure this is the one you install and not any of the others.
The best thing about TIE Fighter is you can play a "bad guy" but not one who is psychopathic or chaotic evil. Every action you take is a lawful one, intended to bring peace, order and stability to the galaxy. The Rebels are thieves and terrorists. The dialogue is fully voiced, an impressive feat for the time, and the missions come with all kinds of twist and turns - not just missions like go here and blow up a ship like X-wing.
2. Knights of the Old Republic II - The Sith Lords
The best writing Obsidian have ever done, fantastic atmosphere, incline on KOTOR in every way - story, companions, reactivity. If you buy it from Steam you'll get the new patches they released this year, which fix some bugs, add built-in support for widescreen resolutions (including interface fixes), and support for The Sith Lords Restored Content Mod (TSLRCM) which is a must have for your second, third, fourth and ninety-ninth playthroughs.
Taken purely from a writing, character and reactivity standpoint, it is one of the best RPGs ever made. It would have been great if Obsidian have been given more time, maybe there could have been proper, multiple endings.
3. Jedi Knight: Dark Forces II
Best shooter of the 90s, great CGI cutscenes, huge levels with verticality and multiple objectives, different endings depending on actions taken throughout the game (and it isn't push button for ending either - the game will assign you light or dark paths depending on whether you kill civilians, and what powers you pick). The expansion, Mysteries of the Sith, had big levels too so it was pretty much more of the same, only without the CGI cutscenes.
4. X-Wing Alliance
Great story that had you running missions in a variety of ships, not just Rebel ships, but doing stuff for your family on the side like raiding rival families, smuggling shit, going to casinos and basically cruising around the galaxy. It was linear but it was possible to explore a little bit when you got to each place. The Rebel missions themselves had some good moments, but not the same level as TIE Fighter. If you buy this from GOG.com, it will work on modern systems with support for modern controllers, and you can download the XWA Upgrade model packs to make everything look beautiful.
5. Jedi Knight II: Jedi Outcast
Best thing about the game is sneaking around and listening to Stormtrooper conversations, then once they are done, Force gripping and throwing them off ledges. Or type in saberrealisticcombat 1 and chop them into tiny pieces with your lightsaber. Game still looks pretty nice today, although the story isn't as good as the others on this list.
Honorable Mentions: Jedi Academy (just like JK2, but with some interesting new level designs, where every mission feels different like Starcraft II is doing nowadays), Bounty Hunter (it was PS2 exclusive, but it had large levels, lots of collectibles, a good plot and good cutscenes), Galactic Battlegrounds (Age of Empires II, but Star Wars), Knights of the Old Republic (a good RPG, even though KOTOR 2 beats it in every way)