The odds of over $1 million in damages are slim, but an umbrella policy wouldn't hurt if it helps you feel better. Most accidents are $2,000 to $5,000 in property damage + up to $10,000 in medical bills and "pain and suffering." The highest auto policy I've seen is $250,000 per person/ $500,000 per accident. To get to a million, I think you would have to have an accident that permanently disabled a young working parent. Obviously this does happen, but it's not very frequent.
Let's say someone uses your car and the damages do go that high. The driver is liable for those damages, they were negligent, not you. The insurance covers them. You might get sued, but RelayRides will pay for your lawyer, and you'll get out of the case because you didn't do anything that was negligent. If the damages are 2 million, then the Plaintiff should go after the driver's property/wages/other insurance, not yours.
What could you do that would realistically subject you to liability? Allow someone you know is a dangerous driver to take the car (negligent entrustment) or fail to do some maintenance you knew or should have known was required which caused an accident. I assume to rent a car with RelayRides people have to apply and be approved. So RelayRides is probably taking care of the negligent entrustment thing by checking driving histories, etc. If you are worried about maintenance, I would try to drive the car a 10-20 miles once a month to be sure you know how the brakes and steering feel, and take it in for scheduled milage maintenance as recommended by the manufacturer.
So it's not impossible, but it is unlikely. To get umbrella insurance you'll likely have to max or raise the limits on your car and home/renters insurance first, and then get a 1 million policy at about $150 a year. If you think you can make about $1000 a year renting the car, you'll probably come out breaking even with a "free" car to use when you want it.