Which successful startup ideas that cross cultural barriers can be started in developing countries where there is little to no competition (and the market is up for grabs)?
I would say a (daily/weekly) deal site, e.g. a variation of Groupon, Lifebooker, Google Offers, Amazon Local, AppSumo, etc. Known model that is relatively easy to replicate without big upfront or operational cost. Focus on categories with high profit margins like beauty services, but lower your fees/cut for something as popular as dining to just get to more customers. Education/training (short classes) is also a good category for deal site. You could probably make a good profit margin, if not reinvesting too aggressively into growth Groupon-style. You would probably want to pay close attention to security of the coupons and teach vendors to validate the #s on the coupons before accepting to avoid copies.
Building up a customer base in a given local market would make the company an acquisition target for the big players. Big players don't have the knowledge of a local market to know what's popular and what the margins might be like. I believe there were some notable acquisitions in this market recently, don't recall the company off the top of my head at the moment.
Here are some: