Before I answer this question, I want to warn the reader. It can be very difficult to compare cultures correctly. My advice to anyone who wants to search for patterns (and explain why these patterns exist) is to try learning about a single culture/story first. Once you have shown that you can learn about one culture, then you will have the skills necessary to perform comparisons and learn something from them.
Have you heard of the Thompson Motif Index? It's essentially a TVTropes for folklore, i.e. a list of folklore organized by motifs. Most importantly, it's available for free online. There are two online versions available: a difficult to use plain-text tool and a database version, titled MOMFER, that is easy and convenient to use. Here's a screenshot of MOMFER (which I recommend that you use: it's so much more convenient) in case you are skeptical:
In case you are interested: the code for MOMFER is available on github and the creators of MOMFER have written a paper about developing the tool (unfortunately behind a paywall).
One issue that might be relevant is that we should not assume that the Thompson Index does not list every instance of a motif (it was published in the 1960s). However, it should be good enough for the purposes of the majority of the visitors to this site.
There are other myth indexes available that focus on specific regions and/or are more up to date. As far as I can tell, those indexes aren't available online, so you will have to look for them in a library.
