It's a bit dumb and kiddified, which is a shame since the last few episodes are saying interesting things about artificial intelligence and death. What really hurts it, I think, is that we've seen quite a few MMORPG anime since this came out and they all outclass it. As well as Log Horizon and Sword Art Online (both excellent), just the last two years have given us Overlord, Grimgar of Fantasy and Ash, And You Thought There Is Never A Girl Online? and Phantasy Star Online 2 The Animation.
(MMORPG stands for "Massively Multiplayer Online Role-Playing Game", in case you don't know or had forgotten. Players from all over the world log into the same gaming universe, which is usually fantasy-based like Dungeons & Dragons but can also be SF, e.g. Star Wars.)
Anyway, for quite a long time, .hack// (pronounced "dot hack") was the MMORPG anime franchise. There was nothing else. Well, apart from Master of Epic: The Animation Age in 2007. (Anime based on table-top RPGs were the in-thing instead.) Dot-hack started in 2002 and ran for a good ten years, with overlapping anime series, video games, manga and novels. The first anime was .hack//Sign and has the reputation of being quite serious and talky. This instalment is more lighthearted and has:
1. Scooby Doo style action, with heroes and goofy monsters chasing each other. (Not all the action scenes are like that, but some are.)
2. Cartoonishly drawn child heroes, although personally I think that's fine since we're in a computer game world. Whenever our heroes return to real life, the art style becomes much more realistic.
3. One-dimensional heroes. There's a sexy werewolf, a little girl who collects rare items and a couple of other people who, um, something. They're a party of fantasy heroes. That's about it. They're good-natured and you don't hate them or anything, but you probably wouldn't notice if any of them got deleted from the show. However you will at least remember...
4. Rena and Shugo, the incest twins. They're also the protagonists. Not sure how that got into a kiddified show. Apparently the manga plays it more for laughs. This has creeped out more than a few Western fans and given rise to the nickname ".hack//Twincest". Personally I found it quite funny and it was often my main source of entertainment in an otherwise unmemorable episode, but: (a) actually it's just unresolved sexual tension, (b) there's not that much of it, and (c) Rena drops out of the plot halfway through anyway. After that it's The Search For Rena, which is less amusing.
As it happens, that's also more or less where the anime overtook the manga. They had something to adapt up to ep.6, but after that they were making it all up. The show develops. More serious stuff happens. Admittedly it went on feeling low-stakes and kind of trivial for a while after that, but at least they were heading in the right direction. More villains appear, one of whom I even liked (the friendly traitor with unreadable motives). Eventually the story becomes worthwhile, with an interesting spin on the fundamental problem of anyone trying to write an MMORPG anime, i.e. death isn't death, nothing is real and your characters can just log out at any time. Someone's trying to understand the meaning of death. I quite enjoyed the final episode.
That said, though, the show as a whole still feels a bit Saturday morning. For example, I disliked the bit in ep.9 where our heroes try to be inconspicuous by dressing up in frog and rabbit costumes. That's not funny. Instead it's the kind of thing that's being flagged up as "funny" in bad children's cartoons. I have a similarly low tolerance of Mr Tres Bien.
I like the comedy music in ep.2, though. It's the most entertaining thing in the episode. However "shindara kawaisou" the week after is a stupid line.
This isn't a terrible series. I just don't think there's much point in watching it, especially since there are other, better MMORPG shows you could be watching instead. I'd recommend Log Horizon or Sword Art Online... and that's without considering closely related anime like Is It Wrong to Try to Pick Up Girls in a Dungeon? It might perhaps be worth watching for completeness if you're ploughing all the dot-hacks, being the last story to date set in The World R:1, but then again the most vitriolic reviews of it I've seen have been from fans of the franchise. The Rena-Shugo subtext is good for a laugh or two. The ending isn't bad. Otherwise there's not much here, really.