I don't really have a favourite. I mean, I did form attachments to them but in a platonic intellectual sort of way because seven-way mind games. xD But I'll give my opinions for all characters (that had significant impact on the Holy Grail War).
Spoiler:

King Arturia: Every show needs a heroic paragon and Saber fits that title to a tee. I'm not fond of her, but I'm impressed with the lore-play of her NPs.
Emiya Kiritsugu: The 'Batman' of the series. He was probably the most fleshed-out character with the most interesting development path. His love for Irisviel and Maya - two women who relied on him for support - and his friction with Saber was well-executed and well, real.
Irisviel von Einzbern: More of Saber's Master than Kiritsugu, despite being proxy. I find her naive sense of justice (naive because she was influenced by Kiritsugu) akin to Psycho Pass' Akane. Her growth into someone who can use her beliefs to face stronger challenges was a bit cliche, though I find her quite likable.
Maya: Strong female character with a dark background. I'm going out on a limb by saying she could be Urobutcher's perspective on how women are treated like objects/tools. Her love for Kiritsugu was what made her human.
Tokiomi Tohsaka: Rich elitist but not as much as a douchebag than Kayneth. Typical caricature of the working father who prioritizes business over family. The Tohsakas are the stereotypes of a typical upper-class family, with women being oppressed.
Gilgamesh: Does whatever the f--- he wants because he is the King of Babylon with the greatest treasures. Oh and he's totally not in a homosexual relationship with a priest. I love his fight scenes the most, especially against Berserker.
Kotomine Kirei: Sociopath? Priest? Both? IDEK, he's like Makishima Shougo to Kiritsugu.
Hassan-i-Sabbah: Hardly has anything to comment on except that he has a cool and nearly broken NP.
Alexander the Great: Funniest character with the best charisma and manliest charm. His straightforward brutal force is a relaxed perspective from all the suspenseful strategic fighting.
Waver: I actually like him, only because of his relationship development with Rider. Hands down, the best Master-Servant dynamic.
Kayneth Archibald El-Melloi: #1 Elitist Douchebag. Favourite scene of him was him vs Kiritsugu as well as him vs his wife >:D
Sola-Ui Nuada-Re Sophia-Ri: Best named female ever. xD
Diarmuid: Male counterpart to Saber. I love the ending animations of his legend. And isn't he just the hottest Servant ever?
Ryuunosuke: Crazy killer who was probably just a mouthpiece for the division between atheism and theism, what with all that talk about God being a sadist.
Gilles De Rais: His relationship with his Master is almost symbiotic for pleasure. Creepy Servant, but hey, that's what the lore ordained so no complaints.
Kariya Matou: One of the few Masters with a profound motive (the other being Kiritsugu). He could've greater audience sympathy if the show wasn't set up to lead into the mess titled "Fate: stay/night".
Sir Lancelot: Most awesome NP ever? I love every fight scene with him in it. It moves my black heart. *tear*