Two bug trackers I know:

• BugTracker.NET

BugTracker.NET is a free, open-source, web-based bug tracker or customer support issue tracker written using ASP.NET, C#, and Microsoft SQL Server (or its free cousin, SQL Server Express).

• BugNET

BugNET is an issue tracking and project issue management solution built using the ASP.NET web application framework. Email notifications, reporting and per project configuration of fields and values allows efficient management of bugs, feature requests, and other issues for projects of any scale.

I've used IssueManager from UltraApps. It is free, and open source.

I've actually used it at two of my prior employers.

http://www.ultraapps.com/app_overview.php?app_id=20

Thank you all for your answers. Using your answers and other resources on the web, I've put together a method for submitting a new bug to BugTracker.NET

Here's the code:

public bool SubmitBugToBugTracker(string serverName,
                                        bool useProxy,
                                        string proxyHost,
                                        int proxyPort,
                                        string userName,
                                        string password,
                                        string description,
                                        string comment,
                                        int projectId)
    {
        if (!serverName.EndsWith(@"/"))
        {
            serverName += @"/";
        }
        string requestUrl = serverName + "insert_bug.aspx";
        string requestMethod = "POST";
        string requestContentType = "application/x-www-form-urlencoded";
        string requestParameters = "username=" + userName
                                  + "&password=" + password
                                  + "&short_desc=" + description
                                  + "&comment=" + comment
                                  + "&projectid=" + projectId;
        // POST parameters (postvars)
        byte[] buffer = Encoding.ASCII.GetBytes(requestParameters);
        // Initialisation
        HttpWebRequest WebReq = (HttpWebRequest)WebRequest.Create(requestUrl);
        // Add proxy info if used.
        if (useProxy)
        {
            WebReq.Proxy = new WebProxy(proxyHost, proxyPort);
        }

        // Method is POST
        WebReq.Method = requestMethod;
        // ContentType, for the postvars.
        WebReq.ContentType = requestContentType;
        // Length of the buffer (postvars) is used as contentlength.
        WebReq.ContentLength = buffer.Length;
        // Open a stream for writing the postvars
        Stream PostData = WebReq.GetRequestStream();
        //Now we write, and afterwards, we close. Closing is always important!
        PostData.Write(buffer, 0, buffer.Length);
        PostData.Close();
        // Get the response handle, we have no true response yet!
        HttpWebResponse WebResp = (HttpWebResponse)WebReq.GetResponse();
        // Read the response (the string)
        Stream Answer = WebResp.GetResponseStream();
        StreamReader _Answer = new StreamReader(Answer);
        string responseStream = _Answer.ReadToEnd();

        // Find out if bug submission was successfull.
        if (responseStream.StartsWith("OK:"))
        {
            MessageBox.Show("Bug submitted successfully.");
            return true;
        }
        else if (responseStream.StartsWith("ERROR:"))
        {
            MessageBox.Show("Error occured. Bug hasn't been submitted.\nError Message: " + responseStream);
            return false;
        }
        else
        {
            MessageBox.Show("Error occured. Bug hasn't been submitted.\nError Message: " + responseStream);
            return false;
        }
    }

Trac and Redmine both support integration with Git. It looks more or less exactly the same as the Subversion support. The bug tracker follows one repo as the benevolent dictator repo, it doesn't have to care about all the other clones around the place.

One thing I do think is worth mentioning is that any bug tracker needs to support git branches properly. Working on branches is such an important part of the Git methodology, it needs to be supported in the bug tracker. Redmine can do this through a patch, but last I looked (about a month ago), it wasn't in the main source tree (you could only follow master).

Other useful features would be a graphical representation of how branches are created and merged, similar to how gitk looks. I don't know of any bug tracker that does this kind of visualisation.

EDIT by Corey Trager. I copy/pasted @Squelch's answer here (I upvoted @Squelch too):

Due to the distributed nature of Git against the centralized nature of SVN, it is quite possible for every user or copy of the repository to have different branches. The exisitnig trackers typically have a local copy of the repository that is used as a central reference ("benevolent dictator") that can be regarded as the working copy for all users.

It is quite feasible for users to have a different branch structure in their local copy from that of the tracker. They might choose to keep some private, pull only the branches from the remote that they are interested in, or push a new branch to the remote (tracker). Users can even share branches between themselves that the remote may never see.

The bug tracker can really only reference repositories it has access to. Commonly this is local to the tracker, but it is also possible to pull from repositories remote to the tracker, and far harder to manage. If it is accessing a remote, it can only track branches that it has knowledge of, and there is not really a method of initiating this task apart from a scheduled task. This also assumes that users are serving their local copy too.

As you have already noted, a scheduled task, or an event hook can be used to update the tracker using the commit log for details. These details can then be matched to the tracker issues for viewing as required and noted above.

In short, the tracker will typically see whatever changes are made on the branches it currently has access to. With a hook these changes are seen immediately including the creation of a new branch. It will not see or track changes made to users (offline) repositories until they push those changes.

END OF @Squelch

It couldn't matter less to me what technology the bug tracker is built in. I like FogBugz alot, and it's not .Net based. Neither is Bugzilla, and we've used that to track .Net projects.

There's really no point in worrying about the underlying technology of the tools you need to do your job right.

<add key="ConnectionString" value="Persist Security Info=true;User ID=bugtracker;Password=bugs;Initial Catalog=BugTracker;Data Source=[IP ADDRESS]" />

This is what you'd need to add/edit in the web.config. once it's setup, BugTracker will run the scripts to create the proper database elements.