There are several reasons that Dojo was chosen as the foundation for the ArcGIS API for JavaScript:
Dojo is very capable, but there might be times when it is easier or faster to use other frameworks or toolkits. In those cases, you can use those other tools in conjunction with the ArcGIS API for JavaScript and dojo. There are samples in the SDK illustrating how to do this with jQuery.
Also checkout samples using Angular, Backbone and Knockout on github.
If you do not require dijits when using the ArcGIS API for JavaScript, the compact version of the API is worth a look. The compact build of the API is also a good choice if additional JavaScript libraries are being included in an application.