It took me a while, but ultimately I had to vote for Metal Gear Solid. I absolutely love Half-Life 2, and it's one of the absolute best stories in gaming history in my book (as well as having probably the best game physics EVER) but unfortunately it's facing the absolutely massive milestone in gaming that Metal Gear Solid was.
MGS was more than just a great story, great characters, and great gameplay. It changed how games were made. The tried and true formula of running into a level with guns a-blazin' was put aside for the more logical and ultimately IMO more fun stealth solution. One of the first games to truly capture the anxiety and panic of the unreal situations that games like these put you into.
I wouldn't hold it against anyone if they vote for Half-Life 2, but MGS gets my vote here.