Hydrogen forms 1 single bond when there is a s-s overlap which is the greatest overlap but it can also form 2 single bond where there are 2 s-p overlaps such as is $\ce{B2H6}$

As you can see the two Hydrogen atoms in the centre make 2 bonds each with Boron.

The number of a bonds that hydrogen can make is dependent on the type of bonding.

It can form only a single ionic bond.
It can form two bonds when there is overlap involved (covalent bond)
If stability can be achieved it can form a lot of coordinate bonds, but due to it's small size and only a single proton I would think a max of 1 coordinated bond can be formed if we being with an ionised H-atom.

Hydrogen forms 1 single bond when there is a s-s overlap which is the greatest overlap but it can also form 2 single bond where there are 2 s-p overlaps such as is Even in compounds like $\ce{B2H6}$, H seems to make 2 bonds but it doesn't.

As you can see the two Hydrogen atoms in the centre make 2 bonds each with Boron.

The number of a bonds that hydrogen can make is dependent on the type of bonding.

It can form only a single ionic bond. 
It can form two bonds when there is overlap involved (covalent bond)
It can form a single covalent bond.
If stability can be achieved it can form a lot of coordinate bonds, but due to it's small size and only a single proton I would think a max of 1 coordinated bond can be formed if we being with an ionised H-atom.