How can you get Gmail to show the number of unread messages in the favicon? Specifically, are there any plugins for Chrome that allow me to do it with both regular Gmail and Google Apps? I've used Better Gmail and Gmail Alert (both of which use the same underlying script) but they only work on one, only show up to "3+" new messages, and are often out of date.
The Gmail Favicon Alerts 3 user script works on Chrome, as well as Firefox and Opera (although I haven't tested Opera). It will show up to 999 new messages, and works on Gmail and Google Apps, even if both are opened in tabs.
The "Unread message icon" option in Gmail Labs can do this, as well. (It doesn't show an exact number after you have more than 10 unread messages, but it will show something like 10+, 20+, 70+, 100+, etc.) No browser extensions/plug-ins are needed for this method.
You can enable this for each individual Gmail or Apps account by going to
Settings -> Labs -> Unread message icon and clicking
This works well with Chrome's "pin tab" feature to always show your e-mail in the corner of the screen.
The best of these I've found is the Better Gmail 2 extension for Firefox. Otherwise, the best extension out there for Chrome is the Better Gmail extension you mentioned, which is actually inspired by the Firefox one.