Being the pedant I am, Chili Monster's answer that "another engine" is required for IFR is true for helicopters, but not fixed wing - unless the fixed wing is flying commercially (I think that excludes even freight work, but someone else will correct me I'm sure).
In my experience, some instrument instruction is undertaken in all helicopter types - it's an item in the type rating test to complete a turn on instruments - but the moment you lose sight of the surface, it becomes illegal.
To summarise:
F/W - IFR s/e and m/e, dependent on the avionics installed.
R/W - IFR m/e only, S/E (with one notable exception being a Bell206 at Bristows used for IR training) no IFR.