Python 2 - 78
>>> def p(N):
... print'\n'.join(' '.join(map(str,range(1,i+1)))for i in range(1,N+1))
...
>>> p(5)
1
1 2
1 2 3
1 2 3 4
1 2 3 4 5
>>> def p(N):
... print'\n'.join(' '.join(map(str,range(1,i+1)))for i in range(1,N+1))
...
>>> p(5)
1
1 2
1 2 3
1 2 3 4
1 2 3 4 5