I do not recommend keeping stock that consistently goes down in price/value. I suggest minimizing all depreciating items (such as cars, boats, etc). We are in a recession and the equity you have in your home today will decrease tomorrow. It's like a non-interest bearing escrow account with accruing charges and fees.
I've owned more than 90 properties and built/developed more than 1,000 properties and large parcels, and I've owned a construction, Architecture, Mortgage and Real Estate company(ies) for 18 years. Believe me when I tell you to invest in something that makes sense. If your home is upside down (or close to it), make the difficult decision. These days rent is much less than mortgage payments, taxes and insurance (although you should keep renter's insurance).