First a few things about this post.  It's limited to games that I've played and that means no XBox 360 games.  It's going to be PS3 heavy, but it's just my opinion, and your mileage may vary.  That being said, my thoughts on Day 1 of Giant Bomb's awards and maybe some anime thrown in for good (or bad measure). 
 
First, my takes on the Giant Bomb awards for Day 1: 
 
2010's 2009 Game of the Year (Giant Bomb Pick: Borderlands, my pick: Demon's Souls) 
While the DLC for Borderlands would earn this title for that game, and deservedly for the site, personally the best game of 2009 that I played this year was Gamespot's controversial Game of the Year choice for the PS3.  No game could be responsible for the amount of hours chewed up, the intense frustration and eventual joy that Demon's Souls delivered.  The oppressive atmosphere, tense combat, crazy boss battles, and absolute thrill of taking down one of the PS3's most difficult challenges was an experience that still sticks with me, and the amount of people I know that I would never expect to be into this game that find their way to it and revel in it's craziness still astounds me.   It seemed like a shoe in until a challenger appeared late in the year that nearly dethroned Demon's Souls, but the experience was still too unique and too much to be overcome.
Honorable Mention:  Assassin's Creed 2  
 
Best New Character (Giant Bomb Pick: Bayonetta or maybe Mordin Solus, my pick: Bayonetta) 
Chaos reigned in Platinum Games' reinvention of the Devil May Cry formula and there was witch responsible.  What seemed nearly exploitative turned empowering as Bayonetta as a character (and as a game as well) reveled in it's own sexuality with a self assuredness that didn't care what others thought about it.  She's like that friend you have who's so confident in themselves, warts and all, that you can't help but want to be around them just because they're not self conscious over every little thing.  That and she has guns, guns on her feet, which she uses to kill angels in such interesting ways.   Just brilliant in every way possible and turned someone who doesn't like this type of game into someone who has a picture of her as their background on this site.  
Honorable Mention:  Monkey and Trip from Enslaved: Odyssey to the West
 
Best Original Song (Giant Bomb Pick: Entrance Music - Pac Man Championship Edition DX, my pick: Soul Phrase by Shoji Meguro/Reiko Tanaka, opening song to Persona 3 Portable) 
Persona 3's story is much darker than Persona 4's and the new intro theme for the PSP version of the game sets the mood perfectly for the darkness that awaits.  Opening with a strong guitar lick that plays almost like a dirge of the horrors that await but still keeping the musical feel to the game. Amusing side note to the song, it's mostly sung in English believe it or not, but good luck picking it up throughout the Engrish.   
 
Best Debut (Giant Bomb Pick: Bayonetta, my pick: Bayonetta) 
Most of what I talked about during "Best New Character" section applies here.  Platinum Games DID NOT CARE about what you thought about this game.  They just made it and it's turned into a hallmark of the companies games in 2010.  Vanquish?  They DID NOT CARE if you thought it was a Gears derivative.  Bayonetta? They DID NOT CARE if you thought it was a Devil May Cry clone.  They set out to make their games louder, faster, nastier, more Japanese, and simply better than the games you'd try to compare them to, and they started 2010 off with a liberal dose of that with Bayonetta.  Absurdity transformed into amusement into respect by the end of it for a company showing that kind of over the top commitment to being as crazy as possible, and if 2010 is any indication, 2011 should continue to be a year to look forward to whatever the fever dreams that grip the people at Platinum produce. 
 
Instead of best PC game which I don't have an opinion on not having played Civ V, Starcraft II, or Cataclysm, here's some Anime related stuff for those interested: 
 
Best Anime Series watched in 2010 not made in 2010:  Naoki Urasawa's Monster 
Great writing, and a series to show people who think that all anime sucks.  The animation is more realistic which would make it a less jarring introduction to Japanese Animation than most of what's thrown around, and the story is smart, gripping, and more interesting than anything else I watched this year.  It's makes me wonder if an anime version of 20th Century Boys will ever be made or if the live action films will be the adaptation we get for that story.  Possibly some PLUTO coming as well?  More Naoki Urasawa is a good thing, and here's hoping that more is what we eventually get. 
 
Best Anime Series watched in 2010 made in 2010:  Togainu No Chi (a.k.a. Bloody Curs or Blood of the Reprimanded Dog) 
Also the biggest surprise of 2010, as it was a series during the fall season that I was ready to write off after an episode saying that at least I gave it a shot.  23 minutes later, Togainu No Chi surpassed everything on the surface that would drive me away from it (Boys' Love series, based on yaoi visual novel, shounen-ai character designs) on the initial strength of one of the best anime opening songs this year (Rose Hip Bullet by Granrodeo, the full version of which which sounds like Japanese Dragonforce on LSD, and by the way, whichever between Rock Band and Guitar Hero puts this out as DLC has my money and hospital bills for broken fingers), the gorgeous animation style and use of color during the show, and the absolute stark brutality of the violence.  IA well told story, and more focus on the toll of the situation than the orientation of the characters made it must watch and I'm looking forward to the final episode which should be streaming on Anime News Network shortly.  As I said, it's the biggest surprise of 2010, and a show that those who like their violence more like Texhnolyze and less like Gantz should watch through without hesitation.