Actually, this depends on the computer and the program that you are using. If for any reasons your program exceed any of these limits, then either errors (underflow, overflow, or NaN - which means "Not-a-Number") or "crashing" occur.  In some cases your program will terminate with an error, in some other cases it may continue with unpredictable (and usually unwanted) results.

Experiment with the following algorithm:

Define two variable
      {   Over=1                   Under = 1
Then iterate until an "error" occurs
     {    Over  =  Over*2      Under = Under/2              
print over, under   }

Try the same excersice in: (a) EXCEL, (b)  Maple and (c) if you can in FORTRAN.
Notice what happens when "underflow" or "overflow" occurs in each case.
If division by 2 or multiplication by 2 does not give you quickly an error use a large number instead of 2. Alternatively you can try raising the number to a power.