When I took my KLR on an 1100 mile ride to Kentucky last spring, I decided to pack my chain tools. I've never owned a chain breaker before, but I bought one "just for the heck of it" when I replaced the chain on my KLR at around 11k miles. During my trip, at around 16k miles (so 5k on the "new" chain and sprockets) the chain let go while doing 75 on the interstate in Virginia. No warning, no noise, and it was a well maintained, adjusted, and lubed chain.
The chain did the same as Pirate660's, and wrapped itself around my rear hub. It did minor damage to the engine cases (just a few nicks and scratches), but almost ripped my rear pannier rack off, and the whipping action of the tail of the chain ripped open my airbox, tore apart my inner fender, and ripped apart all the chain guards and brackets.
I was able to get a ride and buy a new chain, but no sprockets, so I opted for a cheap non O-ring chain, because I knew my chewed up rear sprocket would destroy it quickly. I was able to use my chain breaker to remove links and fit the chain to the bike, and get back on the road. If I didn't have the chain tool, I would have had to have the bike hauled to the dealer.
I know this is a 1 in a million scenario, but I was glad I had the tool, and I would never ride a bike with a chain without having one in the tool kit. Along with the chain tool I carried 2 master links. Once your factory chain wears out and you replace the chain, you will most likely end up with a master link (unless you have a dealer install it and press it together). Having a couple spare master links could come in handy if you were to ever have the master link come apart. Having owned a KLR, I quickly learned that you can never have too many spare parts with you!