As Hack-R said in his answer, Zip files can contain viruses.
You cannot get a virus just by single clicking on a Zip file. Edit: It is technically possible, if you have single clicking to run a shortcut enabled. See the paragraph below.
Double clicking is a different story. If it was a real Zip file and it does contain infected files, you would not be subject to getting a virus unless you tried to execute the infected file. For example lets say you have a Zip file containing a virus, called virus.exe. Double clicking the Zip file would not infect you, but double clicking the virus.exe (and therefore, executing virus.exe) could cause you to get the virus.
There is one other scenario that could be a factor. It is not uncommon for unscrupulous people to fake a Zip file. Lets take virus.exe again for the example. Rename the virus.exe file to virus.zip.exe and you have the default setting in Windows Explorer of hide extensions of known file types, it would appear the file is called virus.zip. An unsuspecting user would think the file is a Zip file, even if it had the wrong icon. Double clicking it would execute the virus infected file.