For example, in this picture (ignore the logo):
I love how the background is cute and made up of small, simple images. Where can I find resources like this background, or how can I recreate it?
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I had misread the original question, and Matt's extensive answer covers the 'finding resources' part of it perfectly. But in case you want to re-create the background pattern yourself, you can do it quite easily using probably any graphic software.
The steps would be something like this:
Edit > Define Pattern.
You could always try Google and search for "vector patterns", "vector pattern backgrounds", or "vector pattern maker". A few sites that come to mind if you are looking for vector backgrounds: