Although there are some uses for Type-A to Type-A USB cables, typically the other end of a USB cable uses a Type-B connector. This denotes the device attached at this end as being the client and because these types of device can vary so much we see much more variation in plug/socket types used.
The original type-B plug is the odd tall plug with the sloping top corners that you typically find on printers. This was extended for the USB 3.0 standard to include an extra bump for some new connections.
The classic miniUSB and microUSB are also variations of Type-B, along with the clunky microUSB 3.0, which uses a normal microUSB connection with an extra plug that carries more power connections.
Variations on Type-B have been far more widely adopted due to the sheer necessity of having smaller plugs at the client device end. Indeed there are many devices that use entirely proprietary shape Type-B USB sockets, such as many of the odd shape plugs used on older mobile phones.