Some of the secret entrances are:

Rolento + Hibiki: Hibiki is tying her shoe, then Rolento appears above her and throws a knife at her, which she dodges.
Zangief + Eagle: They both use whirlwind spin attacks at each other, but bounch off.
Bison + Geese (both are big bosses): Bison has a cloak on, and Geese shoots a Wind Cutter at him. Bison dodges it by blocking it with his cape.
Ryu + Ryo (both almost-clone martial artists): Both start in the center in the air and flip backwards.
Ryu + Ken (pals, trained together): Ryu and Ken are standing together talking, then they bang their fists together good-naturedly and move into position.
Terry + Ken: Terry's hat is on the ground near Ken, and Ken throws it to him.
Terry + Yamazaki (rivals, in a way): Yamazaki throws a knife to Terry, and Terry gets mad and breaks it.
Terry + Geese (Geese killed Terry's father): Geese laughs and beckons, Terry says "Geese!" in a mad way.
Ryo + Yuri (Brother and Sister): Yuri says something defiant and points at Ryo, who covers his face with his hand and shakes his head.
Rock + Geese (Rock: Son, Geese: Father): Rock looks mad, Geese says "C'mon!" and Rock gets madder.
Rock + Terry (rivals): Rock puts on his gloves and says something, Terry sticks out his thumb (in a "Thumbs-Up" way) and says "Okay!"

Capcom vs SNK 2 EO Walkthrough
Capcom vs SNK 2 EO Review