I'm going to take "favourite" at face value, i.e. that I actually like, not just that I am forced to use because the alternative doesn't exist (e.g. my bank's app or the post-office's app) or isn't viable (PDF editors on Android).

Libby, the lending library app. I could avoid it and stick to physical media and piracy, but it's a well-designed app with a decent catalogue and given that it's a library and not me purchasing DRMed files, I found the ethical proposition there tolerable.