BABYLON 5
I'd forgotten all about it, but my new DVD set reminded me that Babylon 5 won a couple of Hugos in its series lifetime. These Hugos were for Best Dramatic Presentation. The Award for Best Dramatic Presentation is given to: Any production in any medium of dramatized science fiction or fantasy which has been publicly presented for the first time in its present dramatic form during the previous calendar year. In the case of individual programs presented as a series, each program is individually eligible, but the series as a whole is not eligible; however, a sequence of installments constituting a single dramatic unit may be considered as a single program (eligible in the year of the final installment).

The award is primarily focused on the story and the storytelling of the dramatic presentation... it's an award for writing and is determined by nominations from and a popular vote of the membership of the World Science Fiction Society.

Interestingly, Babylon 5 Season 3 episodes "War without End" and "Z'Ha'Dum" both received enough votes to be nominated, but show creator J. Michael Straczynski reportedly declined.

1997
Babylon 5: Severed Dreams (TV)
Independence Day
Mars Attacks!
Star Trek: First Contact
Star Trek: Deep Space Nine: Trials and Tribble-ations (TV)

1996
Babylon 5: The Coming of Shadows (TV)
Apollo 13
Star Trek: Deep Space Nine: The Visitor (TV)
Toy Story
12 Monkeys

Holy heck! I'm kinda stunned given the competition those years. I would've thought that ST: First Contact would've won in 1997, or that Apollo 13 would've won in 1996.