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I was wondering if someone could tell me whether I would use a .gif or an animation sheet for different animations within GE. Prop animations I'm talking about.. flaming torches, water fountains etc..
They are quite realistic particle effects in which i have .avi files that are quite large in length. I also have the frames of the files split into separate .png images...

And if i do use .gif's for the effects.. Does anyone know of a program which can actually compress the animations?

You can use either, it is up to you. I don't use gifs, but that is my preference. I think avi works, so you could use that. If not, you can also use separate frame images with indexed names.

sometimes for a running animation, or enemy animation, it can be better to use a GIF, because the bitmap, or png.... will sometimes jump around a little bit.

That just means the sprite is not positioned optimally. When making sprites, you should make a template, that way you know that each frame is in the right spot and will not jump around. What is happening is that some of the frames are off from where they were in previous frames. Arguably, it is easier when making a gif, but I prefer png, as if made properly they work perfectly.