Howdy all, first post here.
This is a complex question that needs to be more specific. It would help if the OP had indicated what metrics we should use. Aesthetics? Character development? Concept and consistency thereof throughout the series? Originality? Deliverance? Etc?
The different races do not all get anywhere the same screen time and some do not even get the benefit of having a playable companion to chat with; we must inferr our opinion about them via the Codex and interaction with secondary NPCs. On other cases the companion is such an uncommon example of the group it is hard to use it as suitable material to render judgement of opinion on the species.
For example: we interact with 3 Drell, one is an assassin, the other is a would-be assassin and the other is a stealth thief? Are Drell as a species pre-dispised to such roles, is this a coincidence or fruit of Hanar influence? Then there's the Geth. The only Geth we get to interact with (unless "shooting the hell out of it" counts as interaction) is Legion which can hardly be considered a typical member of its kind either in either design, purpose, software or platform. In fact it could be said this character is a subversion of the concept of the group he represents as it was originally presented to us. Wether this was inspired intent or sloppy writting doesn't change the fact the character is a very warped window to make up our views about a whole species.
Then there's the retcons of several species, and the meta-knowledge we have that different people took the helm of design and led into different directions of their original concept leaving us with a puzzle of pieces that don't fit into a coherent whole and who cut your fingers witrh their sharp edges as you handle them.
So that all that in mind and taking into account my personal personal preference for alien Species hinges mainly on how "belivable" they are I'd classified them thus, listing in each category are alphabetical not order of preference.
Note that I have only played the core games with DLC (for ME2 and ME3). I haven't read any comics or novels. I am also limiting myself to species I have actually met in the games. Codex mentions don't count.
- Best Species/Well delivered/Belivable evolution/Coherent/Solid "hard" SF traits
Quarians
Salarians
Turians
To varying degrees all of these races are belivable examples that evolutionary fit their homeworlds of origin, they have recognizable cultures that come off as natural developments and are either original concepts or fit familiar Hard SF niches in a very well executed manner.
Honorable mention: Collectors - as above but exchanging the coherence for a mysterious "secrets best left untouched" vibe, and the exception that the ASSUMING DIRECT CONTROL lava lamp effect skirts off "Hard SF" territory. Still visually and thematical impressive, plus a great meme that sticks in your head whether you love it or hate it RELEASING THIS FORM
- Undeveloped Species/Wasted potential/Turned into a joke/Stock characters
Elcor
Hanar
Volus
Sincere Lamentation: some of these aliens had a "wow! this is a Hard SF genre game!" factor in ME1 that went nowhere or was simply perverted for comedic relief.
Clarification: it is not that they're bad concepts but that they were aborted before getting a chance to mature.
Wishful Expectation: I hope there species are revisited and expanded in future instalments, having member companions in your party would be a great.
Badassely: Of course, this doesn't mean I do not want more Blasto! Comedy is fine if it makes me laugh. By all means keep the Hanar SPECTRE agent as long as you don't limit yourselves to it.
- Worst Species/Nonsensical/Fantasy ideas/Science out the door/pandering to hormones or lowest common denominator
Asari
Korgan
T*ts and asses, cleavage, sex, spandex, pole dancers, magical powers, monogenders with vaginas that are really women, grumbling voices, unrestrained agression, shotguns, mary sues, badasses, blue alien chiks and dinossaurs, the planet Arrakis known as Dune complete with Sandworms but without the spice (wait were does "Red Sand" come from, *please* tell me it ain't Tuchanka)...the list goes on, and on, and on. As aliens species go, the worst thing in the Mass Effect franchise. Being so commonplace they cannot be ignored and subvert Mass Effect from Hard SF into gonzo SF territory. Complete jokes with no place in propper SF, we have enough Elves and Ogres in Fantasy RPGs already, thank you very much.
- Not enough data to render final judgement
Drell
Keepers
Leviathans
Rachni
Yagh
The available material and interaction with members of these species when compared to the rest isn't enough to come to a conclusion about the races as a whole.
DIsonorable Mention: Drell Solipsism - there still isn't enough clarifying data to reach a conclusion but the "memory fits" of the Drell are something that doesn't make to much sense. We only get two contradictory examples of this ability and it is made unclear if the involuntary memory events of Thane are commonplace to the species or a result of individual PSTD. If Thane is a normal example of the Drell in this feature then I do not see how this Species could be functional let alone exist, and would relegate them to "Worst Species" or possibily the "WTF where they thinking?" category.
- Unable to render coherent judgement due to multiple contradictions and rectons when taken as a whole
Geth
Reapers
As evidenced by years of debate and discussion in forums these two species, when ME1, 2 and 3 are taken together, lack a coherent concept and presentation. It is also unclear at which point(s) in development the shifts occured or whether some (and which) of the alterations were predesigned or run-of-the-moment. I am therefore unable to make a final judgement apart from saying the final presentation seems like a godawful mess.
- Disonorable Mentions/WTF where they thinking?/Inspired by sleep deprivation or drug use?
Batarians - visual design doesn't really make any sense and looks lazy, same thing for their KILL ALL HUMANS theme and attitude.
Vorcha - why do have stone-age space goblins with shotguns and magical regeneration powers in this game? Is this really the best organic cannon fodder they could throw at us? really?