Please take a day to install version control and teach everybody on the project to use it. It's not that hard. Personally I've not used Git, but I have set up and used other version control systems and they are not that hard to get working. Make sure you choose one that integrates with your development environment. This will make using it virtually seamless.
This will not be wasted time.
The time you will lose when someone overwrites or deletes some code will cost you much more.
If you don't have version control you will also spend an inordinate amount of time backing up your project and worrying about which version everyone has and which version is on the server etc.
If you need to convince your boss make an estimate of the time that it will take you to set up and monitor any non-version control solution and add in the cost of rewriting a few days lost work. Don't forget to add in the cost of manually merging edits from 3 developers working on the same source file and the extra cost of getting that merge wrong. Good version control gives you this for free
Then compare that to the cost of getting version control - nil (if you go open source) and setting it up - 3 man days.
Don't forget that an error later in the project is going to cost more than one early on. If you have to redo the entire project because of a mistake anyone can make this will cost far more than just the rewrite time, it might cost your boss the reputation of his firm.
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
don't go with Git just because its "pretty cool", use it because it solves your problem in a way that fits with your workflow.
As for TFS... Martin Fowler had a little survey.
Anyway, you have to define "security" - do you want to protect the source from unauthorised users, or to put a read-only flag on some areas, or even prevent some people from looking at some areas. You can do this in SVN easily, use VisualSvn Server and you can apply r/rw security controls on any folder in the tree. TFS is the same. Git, on the other hand.. is not designed for this. Git works on the principle that all the source is 'copied' to each developer's workstation, so they get everything all the time. Its part of what makes git special - in that once you have all the source locally, you can merge and branch quickly and easily, but it means you do not get to put the corporate restrictions on it either.
The choice of back-end is meaningless. Use a file-based system, or a SQLServer based system.. its all the same, the level of security access depends on what the tool allows (and your admin policies on the back-end data, a SQLServer with a sa password of 'sa' or even unrestricted Windows auth would allow anyone access to the database).