Double stranded RNA Single stranded DNA
The main differences between RNA (ribonucleic acid) and DNA (deoxyribonucleic acid) is that DNA contains a hydrogen atom where RNA has a hyroxyl (-OH) group and RNA's uracil is substituted for DNA's thymine.  The below image shows several deoxyribose molecules bound together, and off to the side, a ribose molecule. It is the OH group on the bottom right of the ribose molecule that is exchanged for a hydrogen in deoxyribose. 

The structures of RNA and DNA are almost identical, so there is no reason why you can't have double stranded RNA. Similarly DNA can be single stranded. In fact, for DNA replication and transcription, the DNA strands must be separated. dsRNA and ssDNA are most commonly found in viruses. Check out these lecture slides for more about them: http://www.columbia.edu/itc/hs/medical/pathophys/id/2009/viruses2Color.pdf