You can try 'Viper'.. its free and gives some features not in turnitin (like links to the plagiarised work)...
it can be downloaded from http://www.scanmyessay.com/
there are many other open source plagiarism checking softwares available as standalone versions and online.. a google search would be quite fruitful.. (https://www.google.com/search?q=open+source+plagiarism+detection+software)
Such stuff like Viber and other free software does not give trusted results; instead ithenticate.com and plagscan.com I think are the most trustful websites for plagiarism checking, but you have to pay for them starting form small amounts to big ones.
turnitin cannot be downloaded since it is a commercial software. Something that we used for a preceding check was a premier version of plagiarism checker x which we could download. iThenticate was another software we could find, but that was not downloadable too. While the previous one gives good results, it seems to work on a very different algorithm compared to turnitin since we had quite different results. iThenticate is a good software, but it is way less stringent than turnitin showing a difference of close to 10-12% on the lesser side. So, I wouldn't recommend iThenticate either. Also, I have heard that it is best not to use turnitin from another university's student/teacher profile since it would get stored in the database and would report against our original. Hope this helps sir.
If you are meaning a demo version of plagscan, then I don't think it would be comparable to turnitin. I haven't used a premium version of it, but that would again have to be paid anyway.