Length definitely plays into it for me, though it's not a defining factor. It needs to be reasonable. If it's too short it loses value, if it's too long (as you mentioned) it could get diluted. Replay value factors into a game's longevity as well.
Story is usually a big one for me but it really depends on the type of game it is. For example, a game like L4D is not about story. Originality is appreciated but lack of it is not a serious deterrent.
If I had to choose one characteristic that I could not do without it'd have to be overall polish. A game has to feel complete and well-crafted. Bugs are inevitable, of course, but as long as they're not game-breaking and can be patched out I can deal with them. The sense that a lot of hard work, creativity, and careful attention went into the development of a game really captures me and gives me the desire to support the developers. People like Blizzard, Bioware, CDProjekt RED, Ubisoft Montréal, Relic and even Epic, among others, stand out in my view because they give me the sense that they genuinely care about their products' quality, the craftsmanship that went into them, and the art of interactive entertainment.
By contrast, you have some games that feel like they've been neglected. My most recent encounter is Divinity II, there's a great game hidden amid the turmoil of bugs, unflattering user interface, and overall lack of polish. Having to dig through the crap to get the jewel can be daunting and it's a real shame.
Another example is Risen, which just feels like repainted a clone of Gothic (though that could be somewhat understandable since it was developed by the same team), it lacks originality in its design from infrastructure to visuals. It felt more like a proposal demo than a finished product.