Well, it's really not a problem with STDIN. The "problem" is that STDOUT has autoflush turned off by default. What this means is that unless you print() something with a "\n" at the end, it won't appear on the screen. There may be a size limit also; e.g., buffers get flushed when you print() more than, say, 2K, but you normally don't hit that with user prompts.
Anyway, to fix the issue, add $|++ at the beginning of your program.

$|++;
print "Enter a number:  "; 
$number = <STDIN>; 
print "You entered $number";
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perldoc perlvar will explain what $| does.

--perlplexer