Why does a sticker slowly peel off, but if it is pulled quickly it tears?
The glue that holds them on flows like a very viscous liquid on long time scales but is stiff on short time scales. If you pull on it suddenly, it acts stiff and holds fast, causing the paper sticker to tear. If you pull slowly, the glue flows and pulls apart before the paper has a chance to tear. This sort of behavior is called viscoelasticity.
Where does this property come from? In a goopy glue of the sort used on paper stickers and the like, the glue is actually a very viscous liquid which readily wets things like paper, plastics, wood, glass, and so forth. If you grab a blob of this stuff and pull it slowly apart, its molecular chains drag and slip past each other and the blob will slowly elongate as the chains slip. However, if you apply a large tensile load suddenly, there's no opportunity for the chains to begin slipping and the glue behaves instead like a chunk of stiff plastic.
Along with niels awesome answer I would also like to add that when a sticker is pulled suddenly and because the sticker is not isotropic, there are parts of sticker which experience the change in stress and strain more than some other parts. Applying large force in short amount of time might cause them to tear a bit , which becomes a weak spot for it and on further application of any force it further starts tear from that edge, which ultimately causes it to tear apart completely
To add to RandomAspirant's and niel's answers, when you pull an item quickly, you are creating not just an acceleration (which provides the force), but what is termed a 'jerk' by Halliday, Resnick, and Krane. The deriviative of acceleration is a jerk :).
Anyway, this jerk - 'j' completely changes the forces on the object. Here F_net= m* Integral(j) + "sticky forces". The first term adds the jerk which contains a time component and likely in this case a spacial component to it. This rapid pull on the sticker then creates a large jerk, creating an even larger force during that small instant when its pulled.
A slow peel however doesn't add this jerk - or at least a very very small one. F=ma due to the stick effect only which is very different.
Also, when a sticker is pulled slowly, when you watch it closely, you will see small filament strands pull up and disconnect one by one. This effectively minimizes the force due to stickiness because only a few of the bonds are being pulled apart by your hand at a given instance.