Guess I'll rank these from worst to best (just my personal opinion, mind you):
5. FMA: Brotherhood- Follows a more conventional shounen story compared to the original 2003 series and I was initially hesitant to watch through the whole show for a while as a result of this. Hype be damned, sticking strongly with the manga doesn't always make for an engaging title.
4. Steins;Gate- Has nice animation and suspenseful moments with Okabe and his partners tampering with time travel and dealing with SERN, but the slow first half does make things a bit of a chore to push through until the more engaging second half comes along.
3. Hellsing Ultimate- An addicting ride of stylish grittiness and over-the-top insanity with the three-way conflict between Hellsing Organization, Millennium and Iscariot, as well as having its moments of excellently animated sequences on par with a movie production. Ranked in the middle because it doesn't have as much depth to it compared to the higher two titles on the list.
2. Death Note- Plenty of fluid and detailed animation in this series and one of the most engaging conflicts I've seen in an anime with the cat-and-mouse game between Light and L over trying to deduce what facts they need to arrest or kill the other. If the events with Near never happened, this would have been #1 among my choices with the poll.
1. Fate/ Zero- An engaging epic ride with highly-detailed artwork, engaging battle sequences, a haunting and energetic soundtrack and plenty of depth into the various Master-Servant relationships and the pasts of several characters who either gain prominent roles later in Stay Night or help escalate the events that would come in that later installment of the Fate franchise.
But in terms of the mentioned categories...
Animation: Fate/ Zero rather easily
Music: A tie between Fate/ Zero and Hellsing Ultimate. The musical choices for Fate/Zero are intense, grand and energetic to go along nicely with its plot twists and battles. But getting to listen to orchestral scores and monk chantings while London is set ablaze from the three way war of factions in the series is really glorious. XD
Characters: Fate/ Zero. Unlike Stay Night, there is greater focus on the chemistry between Servants and Masters that give you different relationship dynamics between the pairings and a number of the major characters in the series get their backgrounds and personalities fleshed out.
Premise: Tied between Death Note and Fate/Zero.
Story: Fate/Zero. The events of the 4th Holy Grail War offered enough twists and shocking developments that kept me hooked on the show all the way to its conclusion. Death Note's premise had more complexity to it that would have outranked Fate/Zero for me if only it chose to end after things with Light and L's rivalry got resolved.