I believe you're looking for the URL Control.  First, register in on your control, with the following:

<%@ Register TagPrefix="dnn" TagName="Url" Src="~/controls/URLControl.ascx" %> 

Then, to setup the control to only allow file selection and upload, use the following:

<dnn:Url ID="UrlFileUpload" runat="server" UrlType="F" ShowTrack="false" ShowLog="false"
    ShowNewWindow="false" ShowUsers="false" ShowTabs="false" ShowNone="true" ShowDatabase="true"
    ShowSecure="true" ShowUrls="false" ShowUpLoad="true" ShowFiles="true"/>
<%-- UrlType is F for File --%>

Hope that helps,

Unfortunately, the URL Control doesn't let you limit the folders that files can be uploaded to or retrieved from.  However, it does respect permissions, so if you have control over the site you're deploying to, you can limit your users to only be able to write to that specific folder.

In terms of what controls are available, I don't know of a definitive list.  ~/controls has address.ascx, dualListControl.ascx, help.ascx, helpButtonControl.ascx, labelControl.ascx, moduleAuditControl.ascx, sectionHeadControl.ascx, skinControl.ascx, skinThumbnailControl.ascx, textEditor.ascx, urlControl.ascx, urlTrackingControl.ascx, and user.ascx.  I've only personally used labelControl, sectionHeadControl, textEditor and urlControl.  In terms of properties, you just have to look to see what's available and what it does, as well as depend on intellisense.

Anyone else know of any documentation on these controls?