Below is a sample code snippet using JavaScript client object model, which gets the list of SharePoint groups the current user is part of.

<script type="text/javascript">
	var clientContext = new SP.ClientContext.get_current();
	var oWeb = clientContext.get_web();
	var currentUser = oWeb.get_currentUser();
	var allGroups = currentUser.get_groups();

	clientContext.executeQueryAsync(OnSuccess, OnFailure);

	function OnSuccess(sender, args)
		var grpsEnumerator = allGroups.getEnumerator();
			//This object will have the group instance
			//which the current user is part of. 
			//This is can be processed for further 
			//operations or business logic.
			var group = grpsEnumerator.get_current();

			//This gets the title of each group
			//while traversing through the enumerator.			
			var grpTitle = group.get_title();

	function OnFailure(sender, args)