The GIF images may be produced with any good image editor. Paint Shop Pro, Adobe Photoshop, Ulead PhotoImpact and Macromedia Fireworks can all produce GIF animations. I'm sure if you hold on long enough those who use them will suggest other programs that may be less expensive or even free, however, regardless of the program being used, there are a few things to consider.
1. Loading messages turn site visitors away in droves.
2. Animations almost always look cheesy and often end up by making a site look very amteurish.
3. It is very difficult to produce valid code when using Flash.
I can think of lots more to add but will leave it at that for now.
The main animation on that page is done in Macromedia Flash. Flash has a horrific learning curve (no exaggeration) and to get yourself up to speed with it to the point where you could produce something along the lines of the intro on that page would take some time and a lot of effort.
The only reason I stayed long enough to view the page was because you had linked to it as your example for this thread. There is a lot of evidence to show that most web users, being victims of the human condition, refuse to wait around for an animation to load up. Anything that takes more than nine or ten seconds to load will normally make your visitor click and go elsewhere. This is not always as much of an issue for the likes of a fan site for sports teams where the audience is normally passionate about the subject in hand, but for most people a loading screen is a real thorn in their side and for dial up web users Flash animations are their absolute bane.
Macromedia Flash would be required for the main animation and any good image/graphocs editing package will allow you to make animated GIFS, once you get your head around the process.
Personally I use Flash rarely and when I do, sparingly, and I never include animated GIFS or sound files on my sites.
It seems like a lot of money and a vast amount of learning time and effort for an animated layout which is actually little more than a 'look at me, aren't I a clever animator' introduction to the main site area. I can't see that it adds value to the site or its content in any way.
You may have gathered that I don't like Flash, at least in this context.
Flash has been one of the most misused and misunderstood applications in the history of web design and development. My take is that if it adds value in some way to your site, its content, your message, products, services or whatever then give it a go. If it doesn't, don't.