I am interested in dropping Visual Sourcesafe in favor of a version control application that offers branching. Sourcesafe's integration into Visual Studio makes checkins/outs a breeze. Can anyone suggest some other programs that offer the same functionality? I would prefer open source but it is not a requirement.
Lots of source control systems offer VS IDE integration. I'm currently using (actually, being forced, almost at gunpoint to use) ClearCase. As much as I loath and detest it, it does offer VS IDE integration, as well as branching.
Try Subversion: http://subversion.tigris.org/ with both tortoise SVN http://tortoisesvn.tigris.org/ for shell intergration and one of either Ankh SVN http://ankhsvn.open.collab.net/ or Visual SVN http://www.visualsvn.com/ for studio intergration.
SourceGear Vault ... nice integration with VS and a very good product ... stores it's data on SQL Server, making it very easy to backup / migrate to other machines/servers.
By far the best source control tool I've used.
SourceGear Vault is very much a replacement for Visual Source Safe. You get the same feature set, and much much more. Additionally it's stable and scales well. But it is very expensive.
Subversion is great for small shops because it's free. The TortoiseSVN client integrates seemlessly into the Windows Explorer shell. But for Visual Studio integration I would promote VisualSVN's plugin. It's not free, but it is very affordable.
Subversion also gives you the advantage of integrating with many other software management tools out of the box.
Subversion. Because, dude, it's like a Time Machine.
Perforce (p4) also offers Visual Studio integration and is a very capable source code control system (although not open source).
Alienbrain also has Visual Studio integration. Wouldn't really recommend it for code, though (it's more designed for art assets).
I know you mentioned open source and this is going at the far end of the spectrum to that but I really like Team Foundation server.
It's not just a source control system but an entire Application Life cycle management tool. It gives you so much more than just source control and unless you are working in a very small team I would suggest it provides value beyond it's price tag.
If you're moving SourceSafe, then Vault is a really smooth upgrade path. It's designed as a SourceSafe replacement, so all of the things you used to use in SourceSafe (including IDE integration) are there (along with some new stuff).
It also has an import tool that will bring in your SourceSafe data along with version history. It's not open source, but it is pretty cheap for a version control system.
My vote is for Subversion because it does what you need and nothing more.
Alternatively if you are a bit more adventurous and require a more complex branching strategy you can check out git.
While Subversion is gaining a pretty big following, we use AccuRev. It's simple to use, has nice graphical editors as well as Visual Studio/File Explorer integration. It ain't free though.
The options that have been mentioned are all good; StarTeam is another option with integration (although not for 2008 yet).
I have used both Subversion and Team Foundation Server extensively, and even though TFS is very tightly integrated into the IDE, I would recommend Subversion. TFS lacks a couple of features that Subversion has, that I really miss - the biggest being the ability to share code across multiple projects using the svn:externals property. TFS does not have this, and this has forced us to structure our source tree in a somewhat artifical way, so as to not have to copy GB of stuff every time we create a branch. I hear that Subversion's integration into the IDE is much better now than when I last used it. I would also mention that if you need work item tracking and other ALM features like that right in the IDE - then TFS may still be the best way to go for you- it all depends on your particular needs.
Go for Plastic SCM. It's very easy to use, it's one of the strongests using branches and one of the few enabling true distributed development from withing VStudio. Great refactor support (move tracking, merge tracking and so on), try moving files from VStudio and so on, and it's free for open source.
I recommend you try SourceAnywhere. It's designed as a replacement for SourceSafe and integrates with Visual Studio well.