I've been a fan of the Elder Scrolls since Morrowind, so I'll probably be a bit biased here. I'm sure everyone else has read mostly what they know from the past few months. So I'll be brief.
Skyrim gets about everything down for an enjoyable experience. The game is not frustrating to pick up and the learning curve does not take long to get over for new players. Returning Elder Scrolls players should be able to slide in quickly. I was a bit disoriented with the removal of the old leveling system of having to get increases in 10 major skills and then investing in an increase in one character attribute, but I think the new system works fine. It has let me go more into the game besides the min-maxing I used to do in previous installments. Controls are pretty easy to pick up, and on the computer it is customizable. Perks are an interesting feature which can in a way challenge players to focus their development in a certain set of skills, so this balances out in a way the ability to become a 'jack of all trades' in the game.
Graphics are fair. Considering the scale of the game, it's understandable why they are not higher resolution, though I think this should have been included when the game launched rather than released some months later. I am alright with how they appear, though I know this was one of the first things people began to change, as it was apparent this was done with the limitations of the consoles in mind. Characters are at least much more easier to look at than Oblivion's.
What I've found surprising is that the game can still hook you, even after finishing many of the quests. There's a lot to see and do, and it really feels like a big world. I would have preferred for the main faction quests to have been a bit more fleshed out, as some of them felt short. I do welcome the 'radiant' quests as a well needed feature to help provide something to do with a faction long after you have completed the main quests which Oblivion and Morrowind lacked, though this random generation can not be relied on to make a fulfilling experience. Thankfully, mods come in handy here to make the game more lasting. Bethesda released the creation kit after the game's release, rather than at launch as with previous installments, which left players to use other tools to make some mods in the mean time. However, what support Bethesda is giving is much appreciated, considering the position of many developers currently towards player-generated content. Bethesda is much more involved with the community it seems now.
The main flaws I had with the game, besides the graphics, was with bugs. Compared to previous games, Skyrim actually seemed to have launched with less problems. The main issue I had was with some quest breaking bugs (such as Blood on the Ice before the patches came in) and some performance issues. Thankfully Bethesda has been attentive in releasing patches, and I hope this will continue even as DLC are released in the future.
It may not be the most 'in-depth' RPG, indeed it's not too challenging once you figure it out, but it's a nice game to explore and dungeon delve in, and has allowed me to kill many hours with.