Music can be structured in many different ways including 12 bar structure which is very common and is mainly seen in blues and rock music. This structure normally follows 4 bars of the 1st chord 2 bars of the 4th chord, 2 bars of the 1st chord followed by 1.
Another common structure is the A,B method; for example in a AABA structure the first section once around the second section then once around the first section again.This is a very common method of giving music structure it can often be seen in charts and standards in real books and so on.
Jazz often follows a variation of this structure. It begins with a head, which is a section containing a melody and hook. After going through the head the musicians will then take solo over the head structure. After all solos have been taken they will return to the head to end.
Music can also be structured around a riff. This structure is created by starting with a riff. The music then builds around this riff people often take solos over it until the piece ends. The riff does not completely change but variations will be added to it as the piece builds and evolves.
A piece can also be through-composed, meaning that there is no defined structure and that the composition follows the stream of consciousness of the composer. Although describing this as a structure is slightly oxymoronic due to the basis of it being the lack of defined structure I believe that once recorded a piece written in this style can always be ratified in some manner.