Are there any apps which support both PDF and EPUB files?
I've tried Alkido, Laputa, and StarBooks, they only seem to support either PDF OR epub, not both.
Aldiko is a good free application for reading PDF and ePub documents.
Both Aldiko and FBreader support PDF reading without conversion. As the app should update, you can check them again.
I found these later: Aldiko only supports non-DRM'd EPUB. NOOK for Android by B&N and Kobo eBooks seem support both PDF and EPUB.
Get the information from: http://www.pdfmate.com/read-pdf-with-ebook-reader-app-for-android.html
I am using BlueFire Reader. It is free of charge and can display PDF and ePub files with Adobe DRM.
Moon+ Reader in the Pro version supports almost all formats available, including ePub and PDF. You can even highlight and annotate text; with PDF files, these highlights/annotations will be directly embedded into the file (so you then can simply transfer the PDF to another reader and have your notes included), while for the other formats they are stored separately. Support is pretty good, fixes and new features are constantly released (developer is quite active and responding).