Devs need to have multiplayer be an afterthought after designing a core, solid single player experience. Either that or have an established user base or famous IP behind the multiplayer.
Take Halo for example, it started as a great single player story with a great combat system (and a second buddy allowed to bum around with you but not shown on cutscenes), and local multiplayer that became extremely popular.
Halo 2 followed the story (but was considered a story flop compared to the first) but turned the multiplayer into quite possibly one of the most thriving multiplayer systems in at least console history. Halo 3 comes around and incorporates even more multiplayer into the campaign, and again continues the multiplayer. It all started with a core single player experience.
COD4, that started the whole FPS as RPG experience, had a comparatively short story mode, but, what a surprise, they started the franchise with COD that was primarily a top notch single player experience. So again, they built upon a successful single player franchise to create a very popular multiplayer experience.
Starcraft, just to point out this isn't limited to FPS, built upon a solid single player experience and was also the first of the craft games to have multiplayer, unsurprisingly it became a crazy hit. Everyone who is interested in Dragon Age has probably mused about how fun multiplayer could be if it was done right. GTA followed this to the T as well, and unsurprisingly most fans liked the multiplayer.
Portal was a primarily single player experience that was lauded like crazy. If they come out with a great multiplayer mode in part deux it will possibly be the next big thing. Plan multiplayer for the sequel seems to be the most direct way to make cash moneys. Or at least focus on the single player first.
The only thing is, there do seem to be some exceptions. Counter Strike, Team Fortress 1+2 for example, but those could be attributed as the "real" multiplayer modes of half life and HL2. Shadowrun was completely multiplayer and was a hilarious flop (even though the gameplay wasn't bad).
Are there any extremely successful multiplayer games that either didn't have a extremely successful single player experience that preceded it, a strong pedigree or were popular PC mods?