The grapevine is always active in tough economic times, but one way to hurt your career prospects is to be viewed as one of its active participants. Companies right now are looking to weed out "bad apples," and if they perceive you as someone who is spreading negativity, you are a target.
If a conversation that you're in starts to get negative, excuse yourself. You should also remember not to talk about co-workers or vent about your company in your office. If you need to blow off steam, do it on your own time.