Google announced on 7/25/2008 that it had indexed over 1 trillion unique URL's. & Bing launched on 2008-2009 that it added over 1 trillion web sites . So maybe add another trillion or more for this last year...
I doubt whether there is any upper limit with modern browsers. There would obviously be a restriction when you fill up your entire hard drive with bookmarks but you are unlikely to meet that in...