Python 2 - 61
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<!-- language: python -->

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