The following answer relies on OS X 10.6 and its new and improved Services feature.
To open URLs from TextMate all you need is a couple keyboard shortcuts. If your cursor is anywhere within the URL or at the beginning (not at the end), you can select the whole URL by going to Edit -> Select -> Current Scope or using the keyboard shortcut ⌃⌥B. Then, in the TextMate -> Services menu, click Open URL in the Internet section. You can set a global keyboard shortcut for this by going to the Services Preference Pane and typing in a shortcut for the Open URL service. I use ⌃⌘L.
Therefore, to very quickly open a URL from TextMate, place your cursor in the URL, type ⌃⌥B and ⌃⌘L. That might even be faster than clicking it if it were clickable.