I don't want to integrate flash in to my website, but I'd like some slick animated (or non-animated) ads on the website. I guess I could use .gif, but it's outdated and not really "open". What other opinions do I have? I want a format that can be animated and have multiple layers, but that is viewable in all browsers...
If anyone can help, thank you.

If you're just looking at adding some animated images, then .gif is probably your best bet. The Unisys patent on it has expired now, so it's pretty much open again. And no other format that I know of both supports animations and are supported by all browsers.

If you're looking for more fancy effects, then you should probably look at some variation of dhtml or javascript or something. I really don't know much beyond that point.

As an aside, you might want to keep in mind things like usability and accessability issues if you decide to go fancy. I, for one, really hate flashy effects that add no real value to a site. Reference: Morons in Web Space