Do RNA molecules bind each other?
The difference between RNA and DNA is rather small, and both can form a double-helix structure. So if you had two sequences of RNA complementary to each other they would basepair and form a helix.

There were also some ideas to use this for therapeutic purposes, antisense RNA, an RNA oligo complementary to a messenger RNA, can theoretically be used to silence gene expression by base-pairing to the mRNA.