It depends what you mean by double stranded.
If you mean two separate RNA strands, perfectly complementary to one another and existing as a basepaired structure in the cytoplasm, then no. Double stranded RNA like that only occurs in some types of viruses (and cells infected by them... so I guess the cytoplasm of a cell infected by a double stranded virus might have a lot of this kind of double stranded RNA).
However, if you mean double stranded in the sense of a single RNA molecule folding back on itself and basepairing with itself - forming stem loops and more complicated structures - that kind of RNA double-strandedness is extremely common. All tRNA's and rRNA's for example exhibit this kind of double-strandedness. Nucleic acids are unstable in single stranded states and will spontaneously fold back on themselves if there is no other strand to basepair with.
Nucleic acids are inherently unstable in a single stranded state. Thus,