There are many different methods of animation:

1. Animated gif, one file containing slices of the animation (you can probably find some examples online of cartoons that do this)(requires no programming)

2. Cycling through a series of jpegs or pngs with jquery (requires some programming)

3. Cycling through sprites in a single jpeg or png with jquery (requires some programming)

4. Flash (which is usually a means of doing some of the above)

5. Movie file

I am sure there are other methods of doing the same sort of thing.

Animated Gif, After Effects or Flash.

Googled 'Animated flame' and 'Animated Dripping Faucet' and got these-

http://bestanimations.com/Nature/Fire/Flames/Flames.html...

http://www.animateit.net/details.php?image_id=3662...

http://www.animationlibrary.com/sc/192/Bathroom_Stuff/?page=4...

http://www.heathersanimations.com/fire1.html...