Warning: this review contains mild spoilers.

First impressions:
So, we got another show about people being trapped in a video game. Man, where have I heard that before?

Story: 7/10
Log Horizon is about a group of people who get mysteriously transported into the MMORPG known as Elder Tales, after they have the final DLC patch for it. With people now trapped in Elder Tales, it's up to the main character, Shiroe, to try to figure out what to do in this new world, and how to get home.
You can tell that this show has a very overused idea, that’s been milked to death in recent years, with most shows of its ilk being gamer-empowerment and otaku-pandering crap, that became boring and uninteresting after the first five-ish times this idea got put into practice. Suffice it to say, I didn’t go into this show with high expectations. I must say, though, that upon watching Log Horizon, I was pleasantly surprised to see that presentation and execution of its basic idea was done pretty decently. Not only do they actually focus on the RPG elements and not just on beta males getting lots of pussy or Jesus-kun with hack powers, but they also actually focus on what would happen if you were trapped in your average MMORPG.
The story line itself it's pretty interesting. While the idea of people being trapped in a video game is fairly standard, the idea of trying to establish a basic government and build a community is extremely unconventional. As a bonus, the idea of not having much interest in escaping the game and returning to their (presumably crappy) lives, but rather staying in the game and making the best of it, is a nice touch. The story and presentation were handled quite well, especially in regard to the sociopolitics between the different guilds and the game’s NPCs, and the psychological issues that may arise from being transported to the game world, after all the initial dust has settled. Another thing that really helped sell the story’s believability as a whole is the way the cast treat the former game as their new reality, especially regarding how they try to solve the problems that plague their new society, as you’d imagine people would in real life. One of the most memorable incidents of something like this happening being the extermination of a faction that practiced slavery and extortion against lower level players.
Perhaps one of the fascinating aspects of Log Horizon is the way it deals with the idea of characters’ purpose for living. One of the big problems early in the series is the general public’s boredom and lack of motivation to do anything, as they don’t really have anything to live for or do. This problem is only heightened by the fact that all they have to do to live in the game world is kill a few entry level monsters for gold coins, and use that gold to pay for a inn and food. As a result, due to the lack of structure, to absotutely nobody’s shock, a lot people start destroying shit and killing other players, with next-to-no consequences, with death being a non-issue.
Now a few negatives I. One of the primary factors that prevented me from enjoying the show was the significant lack of tension, especially that resulting from the more prominent character’s immortality, rendering the concept of death semi-meaningless. This problem I have with the show is slightly alleviated by the fact that characters lose some of their memories when they die, but not much. Unfortunately, since this mechanism never gets put to any use, it’s doesn’t really serve any purpose other than to create artificial tension. Another problem I have with Log Horizon is that even though there are tactics involved, there are some parts where the main characters, particularly Shiroe, pull solutions to problems straight out of their asses, under the guise of experience. Because of this, a lot of the encounters felt very one-sided and the feeling of tension was undercut for me even more than with just the previous problem, and it took away from the experience quite a bit. Something that I’m kind of on the fence about is the fact that there are a few romantic moments between some of the characters. While they don’t exactly feel unnatural and I don't find them too bad, they just don't seem to go anywhere, and I feel that they don't add much to the character or story, anyway. The final negative is that it feels like you would have to be a gamer to fully enjoy it, limiting it’s accessibility. Other than that, Log Horizon is pretty much a slice of life trapped in a video game with romcom elements and good pacing.

Characters: 6/10
The main character, Shiroe(real name Kei Shirogane), was somewhat interesting to me. His strategist appeal, as well as his use of the ruthless tactics that earned him the nickname “the villain behind the glasses”, being more than enough to prompt the growth of my initial interest. My favourite display of this trait is probably when he purchases the main hall, where both the bank and a lot of the local guild's’ headquarters are, and strongarms the local guild leaders into conforming to his plan, and forming a government, or else. This action speaks volumes about his character, as it not only displays his level of cunning and tact, but also how meticulous he can be when pulling off a plan on that scale. In fact, this plan is highly reminiscent of something you would find in Niccolò Machiavelli's book ‘The Prince’, so props for that. Despite the machiavellian schemer front he puts on though, it’s been shown that Shiroe has the best intentions in mind with every action he takes, and just doesn’t care about the way he’s perceived by the general public. Besides which, while he may have a somewhat antisocial and reclusive exterior, he’s surprisingly kind to those that he’s close to. My favourite part of the story, where this aspect of his personality is highlighted, is probably when he takes them time to assume a mentor role for some of the community’s younger low-level players, as he not only goes out of his way to protect them, but also takes the time to teach them to defend themselves. This showcases that he does actually have some people skills, even if he mostly prefers to work by himself, but can also have actual comrades that he legitimately cares for.
The side characters are two-dimensional, at best. Some of the series’ ever so lovably trophy characters include the goofball, the tsundere and the gentlemen badass. You can easily tell how stereotypical they are because of how little they deviate from their stereotypes, with the exception of how good they are at being them. However, even though the characters are so cliched, they actually have some pretty fun character interactions, and have their own role to play in the grand scheme of things. It’s made abundantly clear that this isn't just your lord and savior jesus-kun type of character doing almost everything, and the vast majority of the rest of the cast doing absolutely nothing (other that looking pretty, that is) type of story. Every character, and I mean EVERY character, plays some sort of part in the story, and it doesn't come off as disjointed, like a lot of series with such a big cast do, but rather, very organic. The major problem with the side characters, though, is that not all of them get the necessary amount of screen time to flesh them out. This not only stretches the narrative too thin, but also makes the characters kinda suffer a result. Suffice it to say, though, most of the characters are more than fun and cool enough for that not to be a major problem. Their ample amount of energy and personality also really helps gloss over the aforementioned problem. Unfortunately, there are a few character arcs that are still in progress, so while they may go somewhere in the light novels, as it stands, a sizable proportion of the cast ramain lukewarm and undercooked.
Side note: I found a decent number of the characters relatable, in some way or form, as quite a few of them remind me either myself or people I know in real life, which I find pretty cool.

Art: 6/10
The animation was, for the most part, fine. The backgrounds were alright, but nothing really to write home about, as more often than not they’d look unfocused and sometimes even kinda fuzzy, with there only being a few shots in the entire show that looked decent. They’d have these very bright color schemes, which looked nice and all, but were kinda an eyesore at times and could have used some dimming down. The character designs were pretty basic and definitely inferior to the standard for anime of this genre. The most underwhelming thing about the designs being how lacking they were in the cool factor that you’d expect from videos game avatars, specially for the high level characters the show mostly focuses on. I was kinda expecting their outfits or tools to look cooler and more detailed, when compared to everyone under level 50, as in RPGs you generally get better and cooler looking gear the more you level up, but nope, none of that here.

Sound: 6/10
I found the opening and ending songs really annoying at first, but after a while, they kind of grew on me a bit, growing on me so much that now I have both songs downloaded on my PC. Other than that, though, the OST is kind of bland and generic at times, even if it fits with what's going on. (The OST was done by Yasuharu Takanashi.) As for the dub and sub, they were descent, with Nyanta’s dub and sub voice actors being exceptional, as they both do a very good job of capturing the character’s mature, swagger, gentleman badass appeal.

Enjoyment: 7/10
There were a few things I liked about this show, mostly revolving around the way they tap into some of the potential that this kind of setting can have. I liked the political dealings, the more comedic moments and also the fact that every character has their role to play in the newly formed community. I admit, though, that I also like it for the simple reason that it takes place in a video game and I happen to be a massive RPG fa[n].

Overall: 7/10
If you are looking for a trapped in a video game anime that isn't just otaku-pandering and gamer-empowerment, and are satisfied with the kiddie-pool level of psychology, politics and social issues that the show presents, then Log Horizon is definitely for you. However, if you’ve experienced a lot of the tropes typically used in this type of show and you're not into video games, then Log Horizon will probably become a tedious watch very quickly.

Special thanks to my paid in Yu-gi-oh cards script editor, Lonecrit.