I was going to put a sample animated banner at the top here.
Then I realised you'd probably ignore it.
The long 468 x 60 pixel banner format, especially at the top of the text, says, "I'm an advertising banner!" Like most of us, you've probably developed 'banner blindness'.

These days animated banners haven't much chance of getting us to click the button. A pity really.
Animation saves space, because it can say a lot while running on the spot. In fact it can say quite a bit without any text at all, even though the long low format was made for lettering.
Facial expressions and body language can say it all.
All the same, let's face it, animation just doesn't mix with text. Have you ever been trying to read some text on a web page - and an advertising banner kept jiggling up and down in the corner of your eye? It's worst when that advertisement is stuck on a frame and you can't scroll it out of the way. I call that eye spam!
If you want to use the power of moving images, these days you can add video. It's static on the page, and your viewers can start and stop a video at will.
It's all too easy to get carried away by the charms and advantages of cartoon style animation. I used to love making animated banners in their heyday.
If your graphics really insist on getting up and dancing, make sure at least that they steer clear of the text.
Animation should be there for a reason. Sorry, but the reason that you like it isn't good enough. Resist the animation temptation! Pointless animation is bottom of the pops with surfers - or it was until pop-ups - well, popped up.
Animation temptation