I'm sure many people out there have their favourites. Remember that although most of us have been around the block a few times, there are people new to Tigers and also if not new to riding coming back after the the kids have left. I'll start the ball rolling and if there is enough interest I'll edit them together as a sticky.
Triumph Parts Lists -
World of TriumphGood easily navigable original diagrams. Just note that the part numbers are not Triumph OE numbers and you might struggle if you have one of those rare 900i's.
Fuel Consumption Tracking -
Fuelly International and becoming very configurable with the latest update. You can even add the latest into your forum sigs etc. (if that's your kind of thing

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Rain Radar -
RainTodayUK Specific, shows the last two hours of rain specific radar in a loop, so you can get a good idea of where it's going. Gives you the chance to decide to hole up or haul ass, unless it's raining everywhere

Scottish Midge Forecast -
Midge ForecastScotland specific, at least you can be prepared if nothing much else you can do about the little buggers. There is also an iPhone App, apparently Androids are immune to midges.