Scala - 77 59 58 chars
print(1 to 9 map(p=>1 to 9 map(q=>"%02d "format(p*q))mkString)mkString("\n"))
Sorry, I had to do this, the Scala solution by Malax was way too readable...
[Edit] For comprehension seems to be the better choice:
for(p<-1 to 9;q<-{println;1 to 9})print("%02d "format p*q)
[Edit] A much longer solution, but without multiplication, and much more obfuscated:
val s=(1 to 9).toSeq
(s:\s){(p,q)=>println(q.map("%02d "format _)mkString)
q zip(s)map(t=>t._1+t._2)}