A back-propagation neural network is only practical in 
certain situations. Following are some guidelines on when 
you should use another approach: 

Can you write down a flow chart or a formula that 
accurately describes the problem? If so, then stick with a 
traditional programming method. 
Is there a simple piece of hardware or software that 
already does what you want? If so, then the development 
time for a NN might not be worth it. 
Do you want the functionality to "evolve" in a direction 
that is not pre-defined? If so, then consider using a 
Genetic Algorithm (that's another topic!). 
Do you have an easy way to generate a significant number of 
input/output examples of the desired behavior? If not, then 
you won't be able to train your NN to do anything. 
Is the problem is very "discrete"? Can the correct answer 
can be found in a look-up table of reasonable size? A look-
up table is much simpler and more accurate. 
Are precise numeric output values required? NN's are not 
good at giving precise numeric answers. 
Conversely, here are some situations where a BP NN might be 
a good idea: 

A large amount of input/output data is available, but 
you're not sure how to relate it to the output. 
The problem appears to have overwhelming complexity, but 
there is clearly a solution. 
It is easy to create a number of examples of the correct 
behavior. 
The solution to the problem may change over time, within 
the bounds of the given input and output parameters (i.e., 
today 2+2=4, but in the future we may find that 2+2=3.8). 
Outputs can be "fuzzy", or non-numeric.