In a recent update, TextMate changed the next/previous tab switching keyboard shortcuts to match the ones that Safari uses:
[CHANGED] Change next/previous file tab key equivalents to shift command [ and ]. This has become the de facto standard.
If you use a European keyboard, these are now awful defaults – ⌥⌘8 and ⌥⌘9. I believe that Safari on these platforms uses ⌥^ left & right, but TextMate doesn’t.
This is a pity, especially as there’s a blog entry on their site from 2007 about this exact problem. But never mind, it’s fixable, because MacOS lets you change keyboard shortcuts at a system level.
Open System Preferences, and select the ‘Keyboard’ applet. Pick the “Keyboard shortcuts” tab, and the “application shortcuts” option on the left. Then click the ‘+’. Choose TextMate from the drop-down, and type the exact name of the TextMate menu option to want to override (“Next File Tab” here). Then add the keyboard shortcut you want. Do the same for the other direction.