I have Turbo Tax 2015 loaded but need to purchase the 2016 version, can I do this on line or do I need to buy a new CD?

You can buy either the CD or you can download it. 

https://turbotax.intuit.com/personal-taxes/cd-download/

Or do you want to use the Online web version?  You can start an Online return here.  But there are several big differences between the Desktop program and the Online version so if you used the CD program last year you may not like the Online version.
https://turbotax.intuit.com/personal-taxes/online/

I wish these differences were better advertised. I am having a lot of trouble with the online version including getting any help with my questions and finding old tax returns done through the CD. I re-downloaded my CD and still can't find my last year's return which was obviously filed.

@kylagetz  If you used the CD Desktop program your returns end in .tax2015, .tax2016, etc.  And you should have saved it as a pdf file.  Are you on Windows or Mac?  In Windows the .tax and .pdf files should be in your Documents then in a Turbo Tax folder.  Or search your whole computer for all files ending in .tax or .tax2015.