Can a magnet magnetise an object with greater strength than it possesses? Trivial thought ...
Materials may be broadly superconductive, diamagnetic, paramagnetic, ferromagnetic. An object is magnetized by repetitive motion of a magnetic field across it's surface
Say a field of strength 1T were to be moved across a steel cylinder. Could the field created in the cylinder be greater than 1T? What if the same field were to be applied to a more strongly ferromagnetic material?
 A: Magnetization is the alignment of magnetic domains in the same direction. And as such the field strength depends more on the material. Those that can hold their alignment better make for stronger magnets but they also require a stronger field to align their domains. 
So a magnet can't magnetize anything that is capable to hold a stronger field to a strength greater than its own. Your steel cylinder couldn't even hold a 1T field.  And even if that magnet was moved across a more strongly ferromagnetic material, it wouldn't be strong enough to align the domains to the same strength as your 1T magnet.
A: I tend to agree with L. Motl's comment: theoretically, even in a very small field, the magnetized state of a ferromagnetic can have a smaller energy than a demagnetized state, so, in some situations, a small field should probably be enough to achieve strong magnetization. While I agree that a magnet can stay in a metastable state for a long time, I can see no physical mechanism dictating that the field of the magnetized ferromagnetic must be smaller than the magnetizing field. The following experiment http://www.youtube.com/watch?v=GaD9vAuj20s , where an iron pipe is magnetized in the Earth's magnetic field, seems relevant, although they use some extra "subtle arguments" to talk the pipe into getting magnetized:-)
