Let's say a Spiderman-type character with a Basic Binding attack (binding webs) sneaks up and successfully hits a Nightcrawler-type character (instant Warp) with a powerful Binding Attack. The Nightcrawler-type can't use Move or Change Posture maneuvers. Can the Nightcrawler-type use Warp and move his body out of the binding webs?
Yes, Nightcrawler can escape from the webs by teleporting.
Binding only prevents Move, Change Posture, and facing changes. It doesn't prevent anything that it doesn't mention: it doesn't prevent attacking from inside the webs, seeing out, or using powers such as Warp.
SevenSide Die response is correct except in one respect. The character may still be bound after using the Warp. It depends on how the power is set up. One characteristic of the binding attack is that it can be destroyed by an external force so the referee will have to use his common sense in adjudicating this with the Warp power.
But to reiterate, sans limitations, nothing prevents the target of a binding attack from activating a warp based power.
Rules as written for the Warp advantage allows for a character to carry "up to basic lift, plus any Payload" (B98) No where does it state that when you warp you can choose to not bring something you are carrying with you. But also, no where does it say that you can't intentionally leave things behind.
Can you warp right out of your clothes? Can you warp everything with you but leave all the dirt and grime behind, leaving you cleaner than if you took a shower? Can you warp away, leaving viruses and bacteria behind you?
My call would be "yes...maybe." Give a penalty to the warper based on the size and complexity of what they are trying to warp away or out of. If they fail then the object either comes with them when they warp (if it's <= BL) or they are unable to warp (if > BL.)
Example: Nightcrawler is stuck in Spiderman's net. Nightcrawler gets a -2 because the net is sticking to his body (-1) and covers his whole body (-1). If he fails, he warps away, but the net stays on him (since it doesn't bring him above Basic Lift.)
Example 2: A Nightcrawler is wearing a suit of armor. He wants to warp out of it because he doesn't need his disguise anymore. He takes a -1 because it covers his whole body. He fails, and doesn't warp anywhere because he's at > Basic Lift.
That would be my take on it.