KLR is common and should do it, I prefer the Suzuki DR650 though if you're looking at this class of bike; less 'common issues', lighter, and more dirt oriented.
BUT, I abso-fricken-lutely love my Super Tenere. If I'm going with a few other people, this would be, by far and away, my bike of choice. Yes it's huge, but it'll handle anything you could possibly throw at it, with ease. It has no real 'common issues', a plethora of tire choices, good fuel economy, and dealerships/parts everywhere.
If I'm going alone, even the 650 class bikes are too big (If you can't ride it, better be able to carry it POV required). I'd go down to a strong 250. I have a WR250R, it's plenty strong for some luggage and freeway duty (if needed). It is fuel injected, and while that's all I want around here, in the third world, a carb might be a safer bet.
AdvRider is a wealth of information, but Horizons Unlimited (http://www.horizonsunlimited.com/hubb/) is even more geared towards this type of thing (Round the World trips and Third World stuff).
