I duplicated a few objects with Alt+D and now I want to apply some modifiers to them, however I can't, because they are multi-user objects.
I tried U > Objects but I still can't apply the modifier.
How to make multi user objects single user?
Press U > Objects and Data. Then apply your modifier. Using just Object will make the object a new, separate datablock for the mesh (but will ignore modifiers). However, using Object and Data will make both the objects mesh and it's modifiers a new, separate datablock.
You can also just use Alt+C > Mesh from Curve/Meta/Surf/Text to convert it to a mesh. This will apply the modifier for all instances of the mesh. This means you can get just one instance looking exactly how you want it, use the Alt+C command, and it will be applied to all the meshes.