C# - 117, 113, 99, 96, 95 89 characters
updated based on NickLarsen's idea
for(int x=0,y;++x<10;)
for(y=x;y
99, 85, 82 81 characters
... If you don't care about the leading zeros and would allow tabs for alignment.
for(int x=0,y;++x<10;)
{
var w="";
for(y=1;++y<10;)
w+=x*y+" ";
Console.WriteLine(w);
}