Hitting Tab in Visual Studio selects block instead of adding indentation

Go to Resharper -> Options, in the left treeview select Editor Behavior and uncheck the last option Use Tab/Shift Tab keys for structural navigation.

Update for Resharper 2016.3.1.

Thanks to @Jordan for pointing this out!

This is called Structural Navigation, and is really useful for tabbing between blocks of code, e.g. parameters in a method call/definition - makes it very easy to edit. The behaviour can be changed in the options, under Editor Behaviour. More details in the docs.