I have previously edited Wikipedia without logging in and know people familiar with the project, but I am still learning.
In my opinion, there's still much to be done even if "easy" things like British royalty and every facet of Google's activities are covered. Choose something of interest to you personally (ikhwan is an example in my case), something you've always been curious about (anthropology of art), maybe even something completely different (Wikipedia:Requested articles) and give it a try. I shall be involved more on the curation and maintenance part of the project til I'm more familiar with it, but that's not for want of topics!