To be completely frank (which I'm not, my name's David), the thing I liked best about the HL series was the story. Which was interesting, and varied, and had some characters I really liked, and did a really, really good job of immersing me in the good but fairly abstract FPS game mechanics.
You don't get stories in multiplayer. Sometimes they can pretend there's a story, but it never really works.
I want to know how it ends. Years later, I'm still emotionally invested in Gordon (even though his entire character is inferred from the reactions of people around him!), and Alyx, and Barney, and Dr. Kleiner, and Eli, even D0g, Hedley Lamarr and the G-Man. I want to know how it ends, dammit, especially after the HL2e2 ending (which I am still pleased at having played unspoilered). I want to know more about the Combine and find out what they really want, and see their homeworld (where I'm sure the inevitable climax will be). I want to know who the G-Man really is. I want to know more about the vortigaunts (and hear them talk, which never fails to be hilarious). Basically, I just want to know.
Having a good game would be a bonus too. But mainly I just want the story.