Actually, glasses have very strong ordering of the atoms, but we must be careful of our terminology. Nearly all amorphous materials have very strong order over nearest-neighbor distances. For example, silicon dioxide glass is composed SiO4 tetrahedra connected at the oxygen atoms. The chemical ordering is very strong, with each silicon atoms connected to four oxygens, and each oxygen bonded to two silicons. The bonds are very strongly covalent, and the bulk material displays a band gap of approximately 9 eV. The chemistry between Si and O forces this order.
The order in the SiO4 tetrahedra is truly remarkable, with a very small distribution of O-Si-O bond angles and lengths. This is what is known as Short Range Order (SRO). Any book on glass science will explain how this information can be obtained by x-ray or neutron scattering. Similarly, other oxide and chalcogenide glasses and amorphous silicon exhibit similar strong SRO.
Where the disorder really begins to enter into play is at the Intermediate Range of order (IRO). This is what describes the interconnection of the local structural units, SiO4 tetrahedra in the SiO2 example. In this case the Si-O-Si bonds joining the tetrahedra. This bond angle has a very broad distribution, spreading from about 100 degrees to 180 degrees, with the peak in the disribution being at about 140 degrees. The tetrahedra can also be rotated relative to each other, but I am not going to try to describe that here, in ASCII. Anyway, this is where the disorder comes in. The statistics describing these bonds define the IRO. Also important are the ring statistics, which account for some unusually sharp features in the Raman spectrum of a-SiO2. Vibrational spectroscopy (IR, Raman, and inelastic neutron scattering) provide the primary experimental probes in the IRO domain.
Finally, we have Long Range Order (LRO) which describes the ordering over distances of many atomic spacings. It is on this length scale that glasses truely have no (or very little) ordering.
For an excellent book on the topic, check out "Physics of Amorphous Materials" by S. R. Elliott.