I love my Phil & Ted's Stroller with Doubles Kit. It has decent storage when used a single stroller and great storage when the Doubles Kit is attached and there's only one kid in it (the second seat holds lots of stuff). But when two kids are in it, storage is a problem. What's possibly even more useful than my Stroll'r Swivel'rs is a handlebar console. I bought this one, which is currently selling for $21.99, four years ago when I got my stroller, and I've never looked back. It attaches easily by wrapping velcro straps around the handlebar. It has two cup holders, which I use for sippy cups, water bottles, bags of snacks, flowers my daughter picks on the way home from school, and other miscellany, plus a zipper pocket for valuables. The only problem is sometimes I carry a child up the four flights to my apartment and then realize I've left my keys and/or phone and/or wallet in the console. But I guess that can happen with any stroller. Oh, and it could probably use a washing after four years, but I don't want to remove it and have to be without it!
You can get them for as little as $9.99 or as much as $69.99 (though I don't know why anyone would spend that much. Even the one with built-in speakers for your MP3 player is only $50). I particularly like this J.L. Childress one ($18.97) that has so much storage space it can double as a diaper bag. Whichever one you choose, this is a must-have for any stroller without a built-in console.