I have a lot of PDFs with authors that have accent marks in their names, such as Ekström. I had thought that using the LaTeX code for the letter in my JabRef entries might work since the database is just a BibTex file. No such luck. Turns out you can just use the regular keyboard shortcuts for Mac/Win in JabRef to get the right letters. For a guide to the keyboard shortcuts, check out this about.com link.
JabRef might complain about not being able to encode certain characters when you go to save your database. If so, just chose UTF-8 for the character encoding option. UTF-8 will preserve any letters with accents, as well as foreign characters you might have (e.g. Greek letters in the abstracts).