Q:

Why is DNA double stranded and RNA single stranded?

Why is DNA present as a double helix structure and RNA as a single helix? What causes the difference between them? What are the practical physiological differences between dsDNA and ssRNA? How are the key biophysicochemical features responsible for those differences? What is the role of these differences? Also, why is DNA preferred over RNA as the genetic material?

A:

Though this is a basic question (a few google searches will provide all answers) and you have asked a lot of questions, I shall answer them one-by-one.

Why is RNA single stranded (and not double stranded like DNA)?

dsRNA is less stable than dsDNA.  See this: http://en.wikipedia.org/wiki/RNA#Structure. An important structural feature of RNA that distinguishes it from DNA is the presence of a hydroxyl group at the 2' position of the ribose sugar. The presence of this functional group causes the helix to adopt the A-form geometry rather than the B-form most commonly observed in DNA. This results in a very deep and narrow major groove and a shallow and wide minor groove. A second consequence of the presence of the 2'-hydroxyl group is that in conformationally flexible regions of an RNA molecule (that is, not involved in formation of a double helix), it can chemically attack the adjacent phosphodiester bond to cleave the backbone.
RNAses are very common.  Most critically, in biological systems, the presence of dsRNA is a signal of viruses and active transposable elements, so ssRNA is an easy way for the host cell to distinguish foreign elements.  Yes, that was an oversimplification and ignored functional dsRNA, but even then, dsRNA likely evolved from systems to foreign elements.1

Why is DNA double stranded (and not single stranded like RNA)?

Firstly, the 'information' part of DNA is the nitrogenous base, as opposed to the pentose sugar or the phosphate residues. In a single-stranded molecule, this important part would be exposed to the cellular environment, providing more opportunity for it to be mutated by the various chemicals there. In a double-stranded configuration, however, the two nitrogenous bases are locked within the complex, facing each other in the centre of the molecule. This organisation helps to safeguard them from local mutagens.
Secondly, having two complementary strands facing each other fundamentally means having two copies of the same thing placed right next to each other. This allows for proof-reading. George C. Williams summarised this beautifully in his pithy passage (from "The Pony Fish's Glow" (1997)) (recall that adenine [A] on one strand should always bind to a thymine [T] on the complementary strand, and visa versa; likewise cytosine [C] always binds to guanine [G], and vice versa i.e. Charagaff's rule).2

Source

What is the difference between DNA and RNA?

A complete table of differences can be found here (sadly I can't create a table in markdown) along with this image:

How are roles of DNA and RNA different?

RNA has several different functions that, though all interconnected, vary slightly depending on the type. There are three main types of RNA:

Messenger RNA (mRNA) transcribes genetic information from the DNA found in a cell's nucleus, and then carries this information to the cell's cytoplasm and ribosome.
Transfer RNA (tRNA) is found in a cell's cytoplasm and is closely related to mRNA as its helper. tRNA literally transfers amino acids, the core components of proteins, to the mRNA in a ribosome.
Ribosomal RNA (rRNA) is found in a cell's cytoplasm. In the ribosome, it takes mRNA and tRNA and translates the information they provide. From this information, it "learns" whether it should create, or synthesize, a polypeptide or protein.

DNA's genes are expressed, or manifested, through the proteins that its nucleotides produce with the help of RNA. Traits (phenotypes) come from which proteins are made and which are switched on or off. The information found in DNA determines which traits are to be created, activated, or deactivated, while the various forms of RNA do the work.3
EDIT- As you've asked another question in comments, I will add it here:

Why is DNA preferred over RNA as genetic material?

DNA offered several advantages over RNA so was chosen by natural selection to represent higher beings:

DNA was chemically more stable than RNA so it was possible to maintain greater length of DNA in comparison to RNA. RNA has hydroxyl group (OH) present on the 2’ carbon. This hydroxyl group invites hydrolysis reaction and so it was not possible to maintain long length RNA molecule. This hydroxyl group was absent in DNA leading to stability of DNA molecule.
DNA was more capable in handling self-repair during replication process due to the presence of Thymine instead of Uracil. It was due to the fact that often cytosine was changed into uracil due to the deamination. Now in case of RNA it was impossible for cell to know if uracil should be present there or not but in DNA since Uracil is not all present so it was quite easy to identify the error and rectify that.
DNA also offers more information security because of the double helical structure.4

A comparison of molecular structure of DNA and RNA from here

References:

https://www.quora.com/Why-is-RNA-single-stranded-in-general-and-not-double-stranded-like-DNA
http://medicguide.blogspot.in/2008/07/why-is-dna-double-stranded-but-rna.html
http://www.diffen.com/difference/DNA_vs_RNA
https://www.quora.com/Why-was-DNA-chosen-to-be-the-genetic-material-instead-of-RNA
http://www.atdbio.com/content/2/Molecular-weight-and-mass

