Given you did not provide a more narrow idea of the research you are doing, other than in literature, the answer will not be able to be answered as specifically.
Common themes one can research in literature highly depend on what genre and period you are examining. Therefore, the answer will suggest themes most commonly examined in any literature course or study.
1. Examination of the characteristics common to a specific genre and how different authors create understanding of the themes throughout their own work or as compared to other authors of the same genre.
2. Choose different texts which examine similar themes. Discuss how the authors contrast in their process of highlighting the theme.
3. Take the movie and text of a specific work and examine how the themes are similar or different.
4. Look at poems and texts which have similar themes. Discuss how each author discusses the theme given poems are typically more compact and novels are more drawn out. Which seems to offer the more defined theme.
5. How the examination of themes has changed over time. What were the popular themes examined in the earliest writings as compared to the themes today? Have they really changed that much? Of they have not, why?
As a side note, if you provide a more focused idea of what you are looking for, please post it as a thread and I will be happy to re-examine.