So the endings. (here be major spoilers).
There appear to be basically 3 endings. There's really 4, but if you get the fourth, you didn't really play the game.
1) Shepard merges with the Reapers and controls them, war ends, relays are destroyed. (Shepard dies)
2) Shepard destroys the Reapers (and other synthetics), war ends, relays are destroyed (Shepard can live)
3) Shepard merges life forms, both organic and synthetic, war ends, relays are destroyed. (Shepard dies)
So far as I'm concerned, the third ending is actually pretty good and in line with the rest of the series/game. It plays on the value of self-sacrifices. Mordin and Legion and Thane all provide examples for this, using their lives, and deaths, to help and advantage others, sometimes even others who they have fought or struggled with during their lives. There are other examples throughout the game (Anderson, Samara, Quarian pilgrimages, the Primarch's son, etc). Along with lesser examples of cooperation and altruistic motivations (Wrex, Miranda, Jacob, Liara). And all of this is opposed by the examples of the Reapers and Cerberus working solely for domination or destruction. So it's not like it should have been a surprise. The trick with that ending is that you have to have really worked for it (its not the most challenging ending to get, but it's up there). So people feel disappointed that all their work ends up in a dead guy, or at least a transcendental and legendary character whose place in the story has ended. I guess I can understand that feeling hollow, but it's much better than the other alternatives.
In ending two, for example, if you've saved and advanced the Geth and freed them from Reaper control, they die. And this is especially sour if you saved the Geth at the expense of the Quarians. Most biotics are essentially cybernetic, and it's not explained well how they could survive (that includes yourself). Other advanced artificial intelligences are likely gone (EDI), and so on. That really feels like a cheap out and its the only one where Sheperd can live. Yes, he lives (or can if you really worked for it that is), but trillions of beings are destroyed or diminished by this choice. It's better than trillions more being dead too, but it's not the optimal choice in any utilitarian sense.
As far as I'm concerned, really the worst part of the ending(s) is that all the relays are destroyed. It would seem like ships could still travel through space with available FTL technology, but it would take decades rather than seconds to go all the way across the galaxy, along with absorbing a tremendously larger amount of energy to do it. I cannot imagine that has good implications for the galactic economy, the opportunities of colonies and settlements dependent on trade and resources from far flung empires and alliances, etc. I suppose they could always rebuild them, possibly over many thousands of years. That would be item one on my agenda after rebuilding from Reaper devastation/war on any given planet. Indeed, rebuilding would be substantially easier with access to the global economy than by relying on each planet's easily accessible technology and resources and engineering skills. If the trade-off is that otherwise most everyone is dead, that's fine. But it's still not a fun ending.
I suppose what I would say there is that this is a very strong environmentalist/locavore message underpinning it all. And I find those messages annoying on some level (eg, that trade of resources and commodities somehow destroys the environment or risks global annihilation? A highly dubious contention. Consumption of certain resources does, but that's a different prospect than outright techno-aversions). It also has an explicit technology and humanity cannot co-exist message, a Luddite perspective that runs throughout science fiction as it regards artificial intelligences (other than in Star Trek). I find playing a game in a Terminator+zombies+space epic fun of course, but Terminator I think is technically wrong about the behavior of most prospective AIs and thus overplays the actual probability of fear and warfare and conflict between AIs and organic life, or at least that conflict between varieties of sentient organic life has a high enough probability of destructive and apocalyptic end points that worrying about robot overlords making war on us is not a significantly increased risk to that. Indeed, it was largely the point of the Matrix series too, that machines
and humanity have a useful coexistence for creativity and life, even if
humans have a propensity to use machinery to empower their destructive
potential. Maybe this point isn't very attractive to people.
That kind of over-analysis makes playing games less fun and tends to not happen as a result. I don't think that's why people are pissed about the endings. I think it has more to do with "Shepard dies". Which to me is missing the point of the game and its arc of the story.
Update: There are elements of the ending that make no sense. The fate of the Normandy and your squad is troubling (mostly because that makes absolutely no sense that the Normandy is, well, going anywhere). And, naturally given the fate of the mass relays, the impact that this decision has on the galaxy that you've just fought to preserve is left as a blank slate. We have no idea what happens with the Krogan and their cured status, any love interests that we left behind, or the Geth-Quarian peace, or, to put a fine point on it... Earth. As a comparison, in Dragon Age, the game gives a text summary of what happens to the Elves and Dwarves and Mages that you just united to fight a terrible enemy. We don't get sort of summary or closure to these elements of the story. This is frustrating. The actual endings are fine, it's more that we don't get to see the outcome of those endings.
3 minutes ago