Spiders can NOT fly. . .at least not in the traditional sense.
More Info: Spiders do not have wings and do not travel by their own power, but they can travel through the air in a method comparable to parachuting known as ballooning.
If spiders do not have wings and cannot fly, how is it that species of spiders have been found on remote ocean islands? By casting a line of silk, a spider can travel through the air by allowing itself to be carried by the mercy of a passing breeze. 
A poetic example of spider ballooning takes place in the finale of E.B.Whites’s classic, Charlotte’s Web. Wilbur takes home Charlotte’s magnum opus following her death and anxiously awaits the emergence of Charlotte’s tiny spider babies. Thinking he would have new friends forever he is saddened to realize that soon after the babies emerge, they throw out a line of silk and float away.
An Updated Look at Spider Ballooning
Researchers at the Rothamsted Research, an institute sponsored by the Biotechnology and Biological Sciences Research Council, have developed a new model of this phenomenon. Rather than considering the spider’s line of silk as rigid and straight, the researchers factored in flexibility that demonstrates that it can twist in turbulence changing its aerodynamic properties. This factor indicates that this dragline can carry a spider almost anywhere depending on the conditions of the air on which it is propelled. (“How Parachute Spiders Invade New Territory”, rothamsted.ac.uk)
 “On Six Legs.” Purdue Agriculture. N.p., n.d. Web. 5 Mar. 2012. http://www.agriculture.purdue.edu/agcom/ newscolumns/archives/OSL/2001/November/011109OSL.html
 “How Parachute Spiders Invade New Territory.” Rothamsted Research. N.p., n.d. Web. 5 Mar. 2012. <http://www.rothamsted.ac.uk/PressReleases.php?PRID=19>.