Can afford to travel the world but not afford another lens?
Weight is much more important than cost.
Last time I did 3 months in SE Asia jungle/trekking and all with almost 30 lbs of camera gears (2 35mm bodies & 7 lenses, 1 6x6 med body & 3 lenses, 2 camera bags, 1 camera case, and a tripod). At the end of the trip I ended up with just a 35mm body ++ 50mm prime lens for 2 weeks trekking in northern Thailand rain forest, river rafting, and 4 days on elephants back (and the rest of the gears was locked up in the hotel vault).
I also did a Belize & Mexico trip for 5 weeks with just a Yashica PS (fixed focal lenght Contax/Zeiss lens) and it wasn't bad.
In the next couple of weeks I'm going to Central America for 2 weeks and only arm with the Canon PS S95 (35mm equivalent is 28~105mm).
As said by many posters, any thing in the range or 28~70mm would be adequate ++ a 50mm prime lens, or 24~135mm would be even better ++ 50mm prime. There will be times that you want to use an ultra wide lens but, it is not critical thanks to stitch mode in camera or Photoshop.