Lego if Wikipedia is correct is moulded from an ABS plastic.
It's not the worst to bond, but not the easiest either. Normal epoxies, super glues and polyurethanes will kind of bond it, but not very strongly. Whatever you go for some practical testing is a good idea.
Here are a few options:
Cyanoacrylates (superglues or CAs) need a specific plastics primer for a decent bond. They are not very waterproof. One of the carded glue + primer consumer plastic bonding kits sold by the likes of Henkel/Loctite might be a good bet.
More cost effective if quantities are needed would be one of their bottled industrial CAs with the plastic primer which amounts to the same thing, but you'd have to go to an industrial distributor who would also advise.
They have gel CAs in tubes that are also good with the primer on plastics, and might be a better bet if you are sticking to a porous surface.
There are plastics specific epoxy plastics bonders i think too, with a solvent blended into them to give a bond. Devcon i seem to remember do one but i don't know how good it is.
Araldite have a number of polyuerthanes that reportedly do the job too - products like 2028, 2041 and 2042. Again from industrial suppliers.
A final option as above is a solvent cement that melts the stuff. I don't know anything about acetone, but i think there are purpose made MEK (methyl ethyl ketone - not a nice solvent) based cements for it. A porous surface might cause problems with these too. (or not)
Pressure sensitive films or contact adhesives are also used, but i don't know how good the bonds may be.
Pardon the length, but i've been trawling adhesives for a consulting client recently...
ian
