Should I explicitly remind people to include my name in the acknowledgement? I am a research assistant. I've helped a PhD student from another department throughout her studies by providing and maintaining human cells for her project. She's now about to published, and I'm not sure she would acknowledge my contribution in her papers. Is it acceptable to remind her to acknowledge me? 

Including my name would be good for my future graduate school applications and interviews.
My suggestion is that you could let her know that you would appreciate an explicit ack and that it would help your future, just as you have done here. Don't state it as a duty (which it probably is) but as a professional curtesy and "boost", which it also is. 

You could even write a suggestion of the form of the ack you would like if you would like it to include anything specific rather than just a general statement of thanks. (... who maintained the human cells...).