Higher Octane Premium Fuel -- is it worth the extra money?

My personal opinion, yes, but it depends on your vehicle. In extreme weather conditions most engines will start and run better on higher octane fuels. As well you may see a slight increase in the amount of kilometers/miles that you may drive on the same amount of fuel.
Here in Canada where outside temperatures may reach -50 degrees Celsius with the windchill in the winter premium gasoline makes sense. Last winter I had been using premium gasoline only on my 2010 1.5 Liter VTEC Honda engine and 5W20 synthetic motor oil. Never did I have any cold starting issues during the entire 2012-2013 winter season.
This winter due to higher gasoline prices I have been mixing regular (87 octane) and premium (91 octane) fuels together (still using same synthetic motor oil). There have been at least four instances where my little Honda engine almost did not start, struggling it did eventually. Currently my beloved Honda engine is back solely on the premium 91 octane gasoline and I'm waiting for the next cold spell to see the difference.

I have also tried premium gasoline on a 2009 2 Liter Hyundai engine without variable valve timing system (older technology) using regular 5W30 oil. There was no increase in power on that vehicle, it is hard to judge if there was any extra distance traveled on the premium gasoline.

Here a two articles below with links on regular versus premium gasoline theories and tests:

Article from the Globe And Mail (PRO PREMIUM)
"A car's octane 'appetite' may increase with age. Over time, deposits can accumulate in your car's combustion chamber. In older vehicles, knock may be accompanied by engine run-on. If you hear knocking, a car owner should have their engine checked and/or use a higher-octane gasoline, says Chevron Canada spokesperson Deidre Reid."
"Any of the following can increase the octane level a vehicle may require: carrying or towing heavy loads, driving in low-altitude areas, driving frequent short trips, or driving in high temperatures, says Reid."
"John Thorne, who runs one of the United Kingdom's largest car-tuning services ... Pretty much consistently amongst all the tests - which cover vehicles from 20 years old up to brand new - generally speaking you have an 8 to 10 per cent improvement in power on any car, says Thorne. This generally equates to roughly half of that in fuel economy. It's not an exact science, because it depends on the car, but generally speaking we have been averaging between 5-10 per cent improvement in fuel economy when we had an 8-10 per cent improvement in power."
Link to full article -- http://www.theglobeandmail.com/globe-drive/car-life/do-you-really-need-premium-fuel/article624005/

CBC News article (AGAINST PREMIUM)
Auto expert Marty Stanfel;
"In a test conducted for Marketplace, Stanfel fuelled up a 2013 Chevrolet Cruze — which is designed for regular fuel use — with Shell's regular, then premium V-power gas, and simulated identical drives with each. He found the high octane fuel didn’t burn efficiently and produced extra hydrocarbons, compounds that contribute to the formation of greenhouse gases."
"If they use the regularly priced gas… they’d be saving money as well as doing a favour to the environment, he said."
Link to full article -- http://www.cbc.ca/news/canada/premium-gas-in-regular-fuel-cars-not-cleaner-expert-says-1.1187041

In conclusion it looks as if the higher the technology of the vehicle (Turbo, VTEC, high output compression engine) the higher the octane levels the vehicle will require.