Here are all of the special intros in SNK vs. Capcom: Match of the Millennium.

There are two types of special intros. The first ones shown have unique animation and dialogue:
Kyo vs. Ryu 0:00
Mai vs. ChunLi 0:09
Nakoruru vs. Morrigan 0:19
Athena vs. Sakura 0:28
Yuri vs. Dan 0:38
Geese vs. M. Bison 0:48
Kyo vs. Iori 0:57
Ryu vs. Ken 1:07

The other intros have unique text, but don't have special animations. There are a couple of matchups which share the same text (for example, Leona says "You're through!" to Felicia, Dan and Akari), but I decided to include them anyways for completion's sake:
Kyo vs. Ken 1:16
Terry vs. Ryu/Ken 1:26 / 1:36
Iori vs. Akuma 1:45
Ryo vs. Ryu/Ken 1:55 / 2:05
Ryo vs. Dan 2:14
Mai vs. Morrigan 2:24
Haohmaru vs. Zangief 2:33
Athena vs. Felicia 2:43
Athena vs. M. Bison 2:53
Leona vs. Felicia/Dan/Akari 3:02 / 3:12 / 3:21
Leona vs. Guile 3:31
Yuri vs. B.B. Hood 3:40
Terry vs. Ryo 3:50
Terry vs. Mai 3:59
Terry vs. Geese 4:09
Ryo vs. Yuri 4:19
Haohmaru vs. Nakoruru 4:29
Athena vs. Athena 4:38
Ryu vs. Sakura 4:48
Ryu vs. Akuma 4:57
ChunLi vs. M. Bison 5:07
Guile vs. M. Bison 5:16
Morrigan/Felicia vs. B.B. Hood 5:26 / 5:36
Sakura vs. Dan 5:45
Akuma vs. Evil Ryu 5:55