Mass Effect is not a good example, the number of species in the Mass Effect games quite easily approaches that of your average 4X, and, while it does occasionally lampshade or even outright subvert itself in individual examples (Wrex, Legion, etc), it mostly plays the tropes straight. You have your warrior race, your scientist race, your hot babe who likes to sex everything race, your merchant race, your omnicidal robots, et cetra et cetra. I probably would have considered it a better series if there were no reapers. Am I the only one who saw Mass Effect 3's lousy ending from lightyears away?
Well-done aliens are difficult to find. The only examples I can think of off-hand are virtually every single one from Starbound, the Iskai from Albion, the Treecats from Honor Harrington, and the Vell-os (okay, technically and aesthetically human, but split off from humanity thousands of years ago) from EV Nova.
Animals make great case studies, pick an animal, observe its behavior, the way it communicates, the way it reacts to threats, the way it reacts to its own kind, and try to build a civilization from that. Note that you actually have to observe the animal, because animals tend to act/react very differently than what humans assume. Note that you probably will realize somewhere along the line that, certain traits are simply required in order to naturally build a civilization out of. For example, you can take your average Terran cat, make it anthropomorphic, opposable thumbs, an equal if not superior intellect to humans, and in spite of that you probably will not get a civilization from the results simply because the concept of 'pack' or 'tribe' is simply absent from most felids. A single individual, no matter how talented, cannot build an entire civilization by himself or herself.
If you say that it's not very elegant - or just plain chauvinist - to have so many human-like species and only a similar number of various eldritch abominations, well, you'd be right. But I think games should primarily reflect what players can identify with or are excited to play as, not to make everything symmetrical. A good 4X game with aliens is one you like all races; a bad one is when you feel like sticking to one race (humans) and just beat the hell outta rest.
I think the best route is to have the entire sliding scale occupied. A few near-humans, a few eldrich abominations, and a few that are somewhere in between.
As for 'liking' and 'disliking' races, one of the reasons, in theory, that developers like to throw in a lot of races is because, chances are, different people have different tastes, and the general idea is that everyone will like at least one of the flavors. This theory does hold water, as Starbound, as well designed and interesting as its alien races are, there are a number of people who simply do not like any of the races. Luckily, in Starbound's case, there are mods to fill the gap.
