Steins;Gate is commonly lauded as the time travel story, and one of the best anime and visual novels ever created. Its cultural impact is huge, and its cast downright iconic among the anime community; you'd be hard pressed to find someone that doesn't know who Kurisu is, or who has never heard Okabe's trademark phrase, El Psy Congroo.
#How exactly did Steins;Gate earn its fame? ...Hell if I know.
> The universe had a beginning, but it has no end. Infinite.
Stars, too, have a beginning, but are by their own power destroyed. Finite.
Plot: 7/10
I'll be blunt. This story is extremely sloppy. Of course it is; it's about time travel. Therefore, do not write stories primarily about time travel. At least, not unless you're willing to spend eons making sure everything that happens across iterations is consistent, making sure every mechanic makes sense, and making the story long enough to explain all of these mechanics that allow the time travel to work in a way that actually leaves time for plot to happen. Steins;Gate does none of these things. The saving grace is that Steins;Gate is, in fact, part of a larger series that, from what I hear, is now actually starting to go back and clean up the mess it made, which is great; that gives S;G a lot of potential to be made retroactively better. But as a standalone story, it's littered with contrivance after contrivance that just makes it difficult to take seriously. I've compiled a list of my issues here (full spoilers including the visual novel):
Spoiler, click to view

I am sure that at least some of this is addressed in Steins;Gate 0, Anonymous;Code, or maybe even the upcoming Steins;???, but for now, in this standalone anime, it's damn near inexcusable.
Another issue I have with the plot is the structure. Steins;Gate is, by nature, a character driven story. Its progression relies heavily on Okabe's relationships to the people around him. At the same time, however, this being a story about time travel means traditional character development is damn near out of the question, since events that occur are constantly being undone or redone. The solution to this should be to have a DAMN good main, and very well characterized static characters to pick up the slack. Steins;Gate kind of half succeeds at the former, and doesn't even try to do the latter. I'll get to that more later, but for the time being I'll just say that this story structure is a really cool idea but executed very poorly; there is so much missed potential in it. You may be wondering, then, why I'd give this plot a 7/10. Well to put it simply, it is for Steins;Gate's mastery of two aspects. Its emotional core, and its twists.
Okabe as a protagonist is pretty good, albeit not one of my favorites. Throughout the series a sense of dread and loneliness permeates as it seems that you and Okabe are the only ones who know what's happening at any given moment. It makes him easy to sympathize with and root for, which makes the story's climactic moments just that much more memorable and hard hitting. I can't deny I cried a few times throughout.
Steins;Gate has a lot of twists. Some immensely predictable and bland. Some literal genius. But even the predictable ones get their times to shine. When shit gets real in Steins;Gate it creates this feeling that only a Science Adventure story can. It gets your heart racing. When all you hear is your heartbeat and Okabe slowly turns to look tragedy in the face, the world around you seems to fade away. It's truly something special.
> History teaches us that those who hold wisdom are oft the most foolish.
Characters: 3.5/10
A character driven story should not have purposeless characters among its main cast. Unfortunately, Steins;Gate didn't get the memo. There are two characters among the main cast of Steins;Gate that exist for very little reason; they are given screentime seemingly only to prolong the story. The main plot doesn't make any more or less sense whether you skip their "arcs" or not. This wouldn't even be all that bad if it weren't for the aforementioned structure making the cast very important; but it's made even worse by Steins;Gate's choice to have a cast full of... unapologetic tropes. The obvious standout is Okabe himself. His chuunibyou is very amusing and it carries every interaction he has, and as I mentioned before, his role as protagonist is extremely easy to be invested in. Unfortunately, the cast around him... really doesn't pick up the slack. Kurisu, the sterotypical tsundere with a genius intellect and daddy issues. Stop me if you've heard those before. Mayuri, the airheaded childhood friend. What about that one? Daru, the fat and perverted otaku hacker. Surely you've seen that a million times. I know it sounds like I'm being reductive but for the most part the cast really is just this, and that's among the characters who're important. The ones who aren't... well I'm sure you can guess how shit those two are. Full spoilers ahead.
Spoiler, click to view
Aside from her tropes, Kurisu's role in the story is to always be there for Okabe across worldlines, and it's... not terrible. However, I dislike the handling of her daddy issues, as while it's hinted at rather thoughtfully throughout the show, by the end her dad just ends up being a moustache twirling charicature that undermines this. Her romance with Okabe is extremely forced.
Mayuri's dynamic with Okabe carries the first half of the show; the way he eases up around her is heartwarming, believable, and makes him that much more likeable as a protagonist (as likeable as a self-centered sexual deviant can be, anyway). Unfortunately she gets done super dirty in the second half despite being probably the most important character in the story other than Okabe and Kurisu, and hardly gets any time to shine at all. She herself is never anything more than her trope.
Daru's role as the straight-man to Okabe's chuunibyou is also somewhat entertaining in the first half of the show, but he, too, remains trapped in the confines of his trope and gets a grand total of one (1) good scene (when he sees Suzuha off in episode 16).
Moeka is a plot device. Her role as a Rounder for SERN is extremely obvious from the start and she gets far too little time on the screen for her "redemption" to feel earned whatsoever. She is a nothing character.
Faris and Luka don't matter, and Luka is offensive to boot. See the bullshit list in the plot category. Idea I had regarding Faris:

Suzuha is the best among the cast other than Okabe, as she's an actually somewhat intriguing static character. Her role as John Titor (and Daru's role as her dad) are also practically rubbed in your face enough that I'd be shocked if you didn't predict them, but her journey is an immensely emotional one that gains even more weight when you meet her Beta version. I really like how it's still recognizably Suzuha but a different version that's been through different things and thus isn't the same person, it's very well executed and makes me wish my above Faris idea were implemented.
I struggle to understand why there are completely pointless characters in the main cast that could be effortlessly written out when the actual important characters really could have done with some more time.
> The fish of the sea know not the land. If they too hold wisdom, then they too will be destroyed.
Themes: 4/10
It's a little difficult to take anything specific out of Steins;Gate, unless you want to cop out and say "it's about never giving up" or something cliche like that. I guess if I had to say it's about something, it would be about relying on the people around you even when you think they couldn't possibly understand. I just wish it explored this in a more powerful way. It doesn't really feel as if Okabe learned anything himself from this story. Full spoilers ahead. Spoiler, click to view
You could say he learned not to mess with what he doesn't understand, but I'd argue he did NOT learn that lesson, because if he had, he would've dissolved the FGL. You could say the theme is that there are no villains, and everyone is the victim of fate. Except, that doesn't work either, because Nakabachi exists. It's a strange case where the story feels like it desperately wants to say something, but can't figure out how.
> It is more foolish for man to exceed the speed of light than for fish to live on land.
Visuals and Sound: 3/10
White Fox should stick to Re:Zero and Mushoku Tensei. This does not cut it in the animation department whatsoever. The art style fails to capture the otherworldliness of the visual novel's art, which contributed to the ever present sense of alienation integral to Steins;Gate as an experience. It's still here, but without the original art, it's not as strong. The animation itself is rather low quality, only carried by some surprisingly competent directing.
Sound wise I'm sorry guys but this soundtrack is overrated. Hacking to the Gate sucks and Gate of Steiner is overused and boring. No other tracks matter. Skiiiiiiip.
> Let this be known as the final warning of God to those who rebel.
Conclusion:
While I don't hate Steins;Gate, I also find it very underwhelming. Its strange, self-harming structure, lack of explanations for its concepts, and thematic incompetence set it apart from its Science Adventure cousins, and not in a good way. It's got the DNA, it's got the potential, it's got the flair, the heart of a SciADV story, but it just couldn't quite reach the same levels as its competition, and sometimes for some truly confusing reasons. There's a lot about Steins;Gate I don't get; and I don't just mean its fringe science, but also just... why is it the way it is? Why are there pointless characters? Why are most of the characters so tropey? Why didn't it commit to a theme? Whenever I bring up questions and criticisms like this, the responses I typically get include "it's not trying to be that," or "that didn't really bother me that much." Maybe this is the SciADV elitist in me talking, but I really do think this stuff is worth thinking about, although the mindset makes a lot of sense if you've only seen this anime and not engaged with the rest of the series. After all, a black sheep isn't strange at all if it's not amongst other sheep.
SciADV reading order:
Chaos;Head Noah -> Steins;Gate -> Robotics;Notes Elite -> Chaos;Child -> Steins;Gate 0 -> Anonymous;Code
Read the visual novels, do not watch the anime adaptations of anything that doesn't have Steins; in the name. Both the VN and anime of S;G0 are canon.