Did you get your job by submitting a resume or résumé? While in Spain, did you climb the 11,414-foot Mulhacén or Mulhacen? It depends, I suppose, on who you are, where you're at, and who you're writing for. It doesn't, however, depend on grammar, since while lots of people have an opinion, no one can claim a must-follow rule.
Bill Walsh, a renowned copy desk chief at the Washington Post, says you might as well skip accent marks because to use them consistently would be near impossible (especially for anyone writing on deadline). "English is a language without accent marks," he writes, "even when it's borrowing from languages that do have them." The New York Times style guide begs to differ - it suggests we use accent marks for French, Italian, Spanish, Portuguese, and German words and names only (a Jan. 13, 2007, Times story about Peyton Manning of the Indianapolis Colts referred to his "career résumé"). Some words, it says, retain their accents even after they enter the English language (résumé, protégé) while others do not (facade, cafe), but it doesn't how we're supposed to know which words are in which group.
So here's my advice:
Note: To complicate matters, in Word certain words appear with accents as you type, such as "façade," which automatically receives the cedilla whether you want it to or not. Ditto the words café and naïve, which get topped by the acute accent and umlaut (or dieresis), respectively. I'm sure there's a way to stop the madness, but I have no idea what it is.
Also, and this is annoying, while the Times style guide says one thing, the Times itself is inconsistent, using Sao Paolo and São Paulo, resume and résumé, etc. Still, I'd follow its rule even if it doesn't!