Ellen DeGeneres & Portia De Rossi GLAAD to Be in Love

With Emmys galore already to her name, Ellen DeGeneres can now add another trophy to her shelf – this one relevant to her personal life.

"Love comes in lots of different forms," said DeGeneres, 51, with her wife, Portia de Rossi, 36, standing beside her as the crowd cheered at Saturday's 20th annual GLAAD Media Awards in Los Angeles. "I am flabbergasted by the fact that we're still trying to fight," she added. "I am not trying to fight for gay rights – I am trying to fight for equal rights."

The TV host's award from the Gay & Lesbian Alliance Against Defamation League, at the Nokia Theater, was for the 2008 episode of The Ellen DeGeneres Show on which Ellen discussed her wedding day. Speaking onstage, DeGeneres said, "Portia, I love you."

Others recognized Saturday included an outstanding film award to Milk, a Vanguard Award for Kathy Griffin to her commitment to the gay community, and a best-TV-comedy-series trophy to Desperate Housewives that was accepted by show creator Marc Cherry, actresses Dana Delany and Teri Hatcher and other cast members.

Kathy Griffin Jokes

On the red carpet before the ceremony, Kathy Griffin, 48, told PEOPLE, "I think I’m getting an award for being offensive and fabulous. If there is a gay army, I am their warrior princess. Over the years, the audience has been wonderful to me."

Griffin, known for taking no prisoners during her candid comedy riffs, quipped onstage that no celebrity would agree to present her with her award. She declared, "Everybody turned it down" – including Ryan Seacrest.

"This year, I think Susan got to have a lot of fun with some of the gay character storylines," Teri Hatcher, 44, told PEOPLE of her character on Desperate Housewives. "I do like when Swoosie Kurtz came on and played the gay boss of Susan. I thought it was emotional. That character got to show her struggle and vulnerability."

New Adventures of Old Christine was also cited for an episode on which Julia Louis-Dreyfus played the girlfriend of Wanda Sykes. "I'm so delighted," Louis-Dreyfus, 48, told PEOPLE, "they noticed what we were doing."