Don't ask him. Don't tell him. Show him.
Install svn, or git, or whatever you like on some extra machine. Practice using it yourself until you feel comfortable not just using it, but explaining it. If you're going to make him comfortable with your new system, you'll need to be more than comfortable with it yourself. You'll need to be able to help him recover easily when he screws up a merge or checks something into the wrong place.
When you're ready, show him exactly what you're talking about. Show him that it doesn't "make a mess" of anything. Point out that it doesn't just let you retrieve any previous version of your code with ease, it also makes it possible to know exactly what changed between any two versions.
Point out that if anything ever happens to the server (serious bug, virus, hacker, disk crash...) you'll both look like heros if you can instantly reconstruct the necessary version. Point out, too, that you'll look twice as good if you're able to produce any version on demand. Search your old e-mail and compile a list of problems you've had over the past year that you could have avoided with version control.
Give him a cheat sheet that will make it easy for him to use your version control system.
Finally, suggest some options but leave the decision to him. Should you set up your own server, or use one of the many hosted services? Should you use svn, git, or something else? Should you migrate all seven projects to the system, or try it with one or two at first?
Best Answer
VisualSVN and TortoiseSVN are just UI clients for SVN server. SVN server is source / version control system. Version control system is key asset for any real development because it stores versions of you your source codes. When using version control system you keep only local copy of source codes. The main copy is stored on version control system and you commits changes to the system.
SVN allows:
VisualSVN is extension to Visual Studio which enables you using SVN repository directly from Visual Studio UI. TortoiseSVN is extension to Windows Explorer which enables you using SVN repository directly as you browse folders and files.