Tyler Holmes has an old post on his blog that I felt is with worth mentioning as I faced this problem on a recent project and it is not the most intuitive behavior (but with SharePoint, what is?).
SPWeb.Groups vs. SPWeb.SiteGroups [Tyler Holmes]

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The following is a method to create new cross-site groups in SharePoint 2007/WSS 3.0. Along with creating the group, users are also added to the group based on selections from a PeopleEditor control (better known as the People Picker).

private enum GroupType
{
Owners,
Members,
Visitors
}

public SPWeb CurrentWeb
{
get { return SPContext.GetContext(HttpContext.Current).Web; }
}

private void CreateAndPopulateGroup(string groupName, GroupType groupType, bool createNewGroup)
{
// [...]

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To add a Windows Active Directory Security Group to a SharePoint 2007 or WSS 3.0 site, do the following:

SPContext.GetContext(HttpContext.Current).Web.AllUsers.Add("domain\\Group", "", "", "domain\\Group" );

To add your group to an existing site role (Full Control, Contribute, Read, etc.), use the following:

SPWeb cWeb = SPContext.GetContext(HttpContext.Current).Web;
SPUser user = cWeb .AllUsers["domain\\Group"];
SPGroup grouptoadd = cWeb .Groups["Full Control"];
grouptoadd.AddUser(user);

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To create a new SPWeb (a new site or workspace) and add it to the navigation (Top and QuickLaunch), you can use the following snippet:

SPWeb newWeb;

newWeb = SPContext.GetContext(HttpContext.Current).Web.Webs.Add(strURL, //URL ("foo" would generate example.com/foo)
strTitle, //Title
strDescription, //Description
(uint)1033, // English
strTemplate, // Template type
bUseUnique, // Use unique permissions?
false); // Convert existing web?

newWeb.Navigation.UseShared = (someCondition) ? true : false;

newWeb.Update();

if (newWeb.Navigation.UseShared)
{
Microsoft.SharePoint.Navigation.SPNavigationNode [...]

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