We have a fairly cheap (50$) blender and when we puree food the food constantly sticks to the sides so we have to stop the blender 10 times to push the food back down so that the blades hit it. Is this common, or would a nicer/more expensive blender solve this problem?
The ratio of food to size of container will make a large difference as well as the the texture of the item being blended.
This has been a problem for me with traditional blenders. I've found that an immersion (stick) blender helps tremendously with this in two specific ways:
First, with a stick blender, you are basically holding the blade and can move it around, preventing food from separating and sticking to the sides.
Second, most immersion blenders come with small bowl accessories that in essence give you a "mini blender". Since the bowl is smaller in size, food separating and sticking to the side isn't as much of an issue.
Immersion blenders are pretty cheap -- you can get one for as little as $20. I have the Braun model. It's amazing but I think they stopped making it. The best one on the market now is the KitchenAid.
I use mine for hummus, soups and pestos. It's without a doubt one of the most useful tools in my kitchen.
In short, if you have enough liquid then a good blender shouldn't get stuck and you shouldn't have to scrape it down. Read the answers to my question here - Blender Buying - Square vs. Round Container - that basically addresses the same thing.
Go for a square, glass container with ridges.
While the material of the blender may be partially at fault, this is most likely to happen when blending foods without enough liquid. So yes, it is fairly common and will depend to a large degree on what you are processing. Depending on your desired result, you can also add some liquid such as water or oil to loosen things up a bit.
A similar result with chunky foods is to end up with an air pocket around the blades where they spin freely and the food will not fall down into the blades to be chopped further.