Background:
We've been using Subversion for source control on our extensive ASP.NET project for the last year. It was the fourth tool we tried, and the one that stuck. We have an automated build process and a distributed team. Our repository resides in Minnesota and we have developers in Florida.
We started about 18 months ago with Visual Source Safe, and poor WAN performance led us to try Source OffSite as well as SCCBridge. SOS worked well, but I wanted to investigate free alternatives. SCCBridge was free and looked promising, but I could not get it to work with our server.
We then installed a demo of SourceGear's Vault. I liked the fact that it had a SQL back end. Performance was better that SOS (slightly), but we had a problem with sessions timing out. If you've never seen it, check out their movie trailer.

I've was also evaluating TargetProcess at the time and their road map included integration with Subversion. (I think it was originally slated for November 2005, it's now planned for January 2007). When the demo for Vault was about to expire, and after reflecting on the minor problems, I decided to to install Subversion.

About Subversion Clients:
The trick with Subversion is that there are multiple clients available and you'll need to find the client that is the best fit.
At first we choose two: TortoiseSVN and AnkhSVN.

Tortoise seems to be the overall favorite of the community. It integrates into Windows Explorer. At first, I found this a bit strange, but I quickly got used to it. It provides a rich interface as well as diff/merge tools and frequent updates

Ankh is a plugin for VS.NET. It does not use the SCC API, so I avoided it at first. (Not using the API means that VS.NET doesn't know that the files are under source control.) I did try SVN SCC Proxy, a commercial client that uses the API, but it has special needs. I have decided that I did no mind VS.NET being ignorant about the source control, if you've ever dealt with the Change Source Control dialog box you'll probably agree. (Note: I was still using 2003 at this time.)

I stopped using AnkhSVN after Visual Studio 2005 came out because of compatibility problems, however their sites says that the current release is compatible. Tortoise meets most of my needs. The biggest inconvenience is that when adding new files to your solution\project you have to remember to add them to source control manually. (This could be a big hassle depending on how you work.)

Alternatively, there's a new player on the field, VisualSVN, moderately priced at $19 and integrating with Visual Studio, it looks very promising. However, it is still new and is not yet full featured. Keep an eye on it though.

Of Special Note:
I'm not going to walk through the entire setup process, but rather point out a few caveats. I do recommend not being lazy; read through the manual that comes with Subversion. (The product is different enough from the VSS/SourceGear model to be confusing.)

The most important thing to note is the standard Subversion client (and hence all the third party clients) used a hidden directory to store metadata about files under source control. The directory is labelled .svn.
This chokes an ASP.NET application. Well, it did with 1.1, I haven't tested it with 2.0.
Tortoise provides a special option during their install to use _svn instead. Likewise, Ankh provides a configuration that allows you to specify the directory name. Do not use Ankh to add anything to a repository until you have modified the config file to use _svn.

Subversion uses a Copy-Modify-Merge model. I was used to the CheckOut-Modify-CheckIn model and did not want to try CMM. However, after a week of use, I don't think that I will go back. It is very nice to be able to work when I don't have an Internet connection to my repository.

If you're used to VSS, get acquainted with the difference of vocabulary. Here's a quick cheat sheet:
Check Out - Get an initial working copy. Only used when you're setting up things on your dev client.
Export - Get a clean copy of the project. This means that the local copy with not be under source control.
Update - Get the latest version. This merges changes from the repository into your working copy. It also merges changes into files you've modified, but does not remove your modifications.
Commit - Sends your modifications to the repository.

Finally, be cautious when it comes to renaming, deleting, or moving files. You will want to use the commands provided by your chosen SVN client. Using the native functions or doing things outside of VS.NET can lead to inconsistencies.

PS
During our Subversion setup something caused a problem with Internet Explorer. New Windows would not open properly. Here is an easy fix.

I also recently found msbuild  integration for Subversion at http://msbuildtasks.tigris.org/.  However, I was "integrating" previously using .bat files.