Which business ideas would you go after if you had the time?
"Which markets are under served?"
Well, the ones where:
a) all the current players are offering a value well above what the average buyer wants. (innovator's dilemma scenario)
b) there is a need that is not (well) supported by any player. (blue ocean-y)
None are under served, all have competition - or are illegal, but these still have competition.
So, get used to it.
There are some where a few people with the right talents can make a lot of money for a lon time. But then, this requires rare talents.
Otherwise it is hard work + a LOT of luck. For exmaple Dell - became big in the midst of a freaking crowded markeet already ;)
To answer the question in your post: if I had the time I would love to get into the Operating System market! But then again, I know it will never happen. But that is a market that has a few big players but innovation could definitely break a stranglehold on major player's market share! (think an OS that allows any file type, meaning running native linux, Mac OS and Windows programs all on the same computer at the same time without needing any 3rd party software)
EDIT The reason I know it will never happen is that I don't have the huge amount of time required.
international commercial real estate listings.
There is loopnet, and showcase for usa searches but nothing done internationally yet that has merit.