Quote from Euler:
To be a "universal function generator", you need
neurons => infinity
which roughly implies
examples => 2 ^ infinity == infinity.
So the relative suitability of ANN's really depends on how a LESS THAN UNIVERSAL neural net learns the "true function" you're trying to model, versus some other method (whether it be statistics-based or otherwise).
So you need to pick your model/method well, and hope/verify/compute whether you're not fitting too many parameters.
The goal is most definitely not to learn a 'true' function. You will never know the 'true' function, regardless of how many neurons you have, unless you can some how time travel to the future and have a database of all past/future data; not only is that unnecessary, but it is counter productive.
The goal is to find some kind of relationship
between the three criteria I mentioned, that nets you a positive expectation over time.
If you really want to convince yourself of its effectiveness as a tool:
1) Do some research to understand the basics of what it is meant to do.
2) Read up on some academic papers to get a feel for what has been attempted and where progress is being made. Regardless of what anyone tells you, there are quite a few bright academics around.
Although it certainly pays to be skeptical if you see they sampled a window of 1 year to draw conclusions (kind of like how uptick rule study was done).
3) If you feel you have a rudimentary understanding, there is no better teacher than to build the model yourself and prove to yourself how useful it may or may not be.
And a bit of advice, go back and look at what the most difficult part is-- steps 1->3,
NOT so much the architecture.
If you think a NN is complicated, go back to a simple linear regression and try to understand it's usefulness and/or pitfalls. You'll likely see how the 3 steps are much more important, than the learner. Maybe there are advantages that a NN has over simple regression?
Seeing the truth for yourself is miles ahead of what anyone can tell you. And it is quite easy to build with modern tools that cost you zero. Unfortunately, that is the problem with simply reading 'papers,' they tend to be a bit skimpy on how to actually replicate or build on their work.