Suppose I have a bitcoin to spend. I choose to anonymously give away 1 BTCcent each to 100 people with a bright/crazy business idea, trusting blindly they will one day repay all their profits if their idea takes off. However I don't want a non-monetary product at the end (a la kickstarter), I just want to have BTC returned to me.
I'm literally talking about just sending someone 0.01 BTC after perhaps a minimal background check (say, they have to be a bitcointalk member for at least 1 year to be eligible), trusting they will take the money to build something great.
I support the idea itself, but unfortunately the quantity of funding you're talking about simply isn't enough for true venture capital backing. A venture capitalist, for example, would be more interested in backing, say, 30-40% of the cost to startup a company (with the owner taking on the remainder). If the company takes off and goes public (via IPO or other sale), the VC is able to make quite a bit of money and sells off their portion.
At
BTC1.0 or
BTC0.01 ..or even
BTC10.. you're better off investing normally. A Bitcoin VC would probably look into seeding 100s (if not thousand+) of Bitcoins.
How would I be sure they would repay me and not secretly keep the money?
Establishing a contract between yourself and the individual / company is usually the best way, but certainly not guaranteed. Bitcoin is more or less the 'wild west' when it comes to this stuff.
Second just because it has a new name doesn't mean securities regulations do not apply. What you are proposing is regulated.
In normal markets, yes, you'd be correct. But this is Bitcoin ..investing and trading in various securities is not regulated.