What makes DNA helical?
The helix shape of DNA molecule is a consequence of its secondary structure. This refers to the bases contained in the molecule which pair, thus determining tertiary structure [1].
Basepairing also occurs in RNA, so it can form a double helix. In fact, RNA is composed of short helices packed together [2]. Base pairs maintain DNA's helical structure no matter the nucleotide sequence [3].
A nucleic acid strand is composed of nucleotides joined together by covalent bonds between the sugar of one nucleotide and the phosphate of the next. Adenine pairs with thymine and cytosine pairs with guanine by hydrogen bonds and form the double-stranded structure [3]. Because covalent bonds are stronger than hydrogen bonds, the double helical structure of DNA is easily broken by heat [4], but the nucleotides remain bonded together.
Here is the tRNA molecule (you can see it has short helices):
"TRNA-Phe yeast 1ehz" by Yikrazuul - Own work. Licensed under CC BY-SA 3.0 via Wikimedia Commons.
Here is the DNA structure:
(source: wikimedia.org)"ADN animation" by brian0918™ - Own work. Licensed under Public domain via Wikimedia Commons.

References:

Wikipedia contributors, &quot;Nucleic acid double helix,&quot; Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/w/index.php?title=Nucleic_acid_double_helix&amp;oldid=609435163 (accessed June 26, 2014).

Wikipedia contributors, &quot;RNA,&quot; Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/w/index.php?title=RNA&amp;oldid=612056511 (accessed June 26, 2014).

Wikipedia contributors, &quot;DNA,&quot; Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/w/index.php?title=DNA&amp;oldid=611891356 (accessed June 26, 2014).

Wikipedia contributors, &quot;Nucleic acid thermodynamics,&quot; Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/w/index.php?title=Nucleic_acid_thermodynamics&amp;oldid=606379256 (accessed June 26, 2014).