The resulting rules can be organized hierarchically to share the common rules among the wrappers for the similar websites.
It actually depends on the context surrounding this sentence. Just by reading this one alone, I would imagine this version would preserve your meaning while cutting down on "the"s:
The resulting rules can be organized hierarchically to share common rules among wrappers for similar websites.
If you have qualified "wrappers" to be more specific than "wrappers in general" in another place, then you should post the sentence where you have done that, and the prepended "the" to "wrappers" would be appropriate. If you are just trying to refer to all wrappers used by similar websites, then you don't need to use "the."
I believe for "websites," you should either choose one or the other: "similar" or "the," but not use both. "Similar" qualifies "websites" to mean "websites that aren't much different from the website I'm talking about," while "the websites" means "specific websites that I'm talking about." Both used together would mean "specific websites that I'm talking about which aren't much different from the other website that I'm talking about/have mentioned previously." It is tough for me to imagine a situation where the reader would be so confused about which websites you're referring to that they'd need that much specificity. Maybe if you were talking about a bigger set of websites which then needed to be sub-divided into smaller groups (those which are similar and dissimilar)? Other than that, seems unlikely.
Again, the appropriateness of "the common rules" depends on whether or not you're referring to a specific ruleset, or whether you're just trying to say that all rules which are common in general web development can be shared amongst wrappers. If you are not trying to say the latter, then you should probably remove "common," because in what context exactly are the rules common in that case?
None of these things will make your sentence strictly valid or invalid in terms of grammar, but it will change the meaning of your sentence significantly and may not express what you're trying to say properly.