The humble hydrogen atom is a magnet, a free electron is a magnet and, despite its apparent lack of electric charge, a free neutron is a magnet.
But that doesn't help you much if you want something that can pick the proverbial needle out of the haystack.

When two hydrogen atoms get together - as they like to do - they line themselves up end to end so that their magnetic fields cancel out - as do almost all other magnetic atoms. To get a magnet that you can hold in your hand, you need atoms that will stick together with their magnetic poles lined up. These are the ferromagnetic materials: iron, nickel, cobalt and gadolinium. If you never heard of the last one, it's because its curie point (the temperature above which it ceases to be a magnet) is only 19°C.
Cobalt was once considered to be the king of ferromagnetic materials but, by alloying ferromagnetics with other elements, you can make even better magnets. And so we have aluminium-nickel-cobalt (ALNICO), cobalt-samarium and neodymium-iron-boron. That's useful around here because cobalt is just about the last element you want anywhere near a neutron source.
PS: Many years ago I came across an idea that involved squirting hydrogen ions into liquid helium in a strong magnetic field. The theory was that they might crystallize into solid monatomic hydrogen with all the poles lined up. If this could be done, it would be the most ferocious magnet ever made outside of a neutron star. Such a magnet is thought to exist in Jupiter's core.
PPS: Neutron stars do form with all their sub-atomic poles lined up and they knock Jupiter into a cocked hat.
PPPS: We aren't very good at making magnets. We think MRI magnets are big at a few teslas but a tesla is only one volt.second per sq.m - which is not a lot really.

The problem is our inability to maintain very large electric currents. The solution, as every Trekkie knows, is to use plasma ducts.

If you can confine hydrogen ions inside a tube (using magnets?) and shove them along at a modest rate of one gram per second, you have a current of 96,520 amps. Form that into a coil and you have the kind of magnet that would strip the haemoglobin right out of your blood cells!
