It's a good idea to bring an all weather jacket. The weather seldom stays the same for long, and once you've desided to go out it might turn from sunshine to rain and wind. You should prepare for all kinds of weather in the summer: Bring both the t-shirt and the warm pullover.
Photo Equipment: Depending on what you are going to take pictures of: A polarizer might not be a bad idea.
Clothing/Shoes/Weather Gear: Firstly, the weather in Trondheim is like a woman's mind; changing all the time! This means bring all kinds,'cause all 4 seasons may come in the same day. This picture of the Monks Island can be either from spring, summer, fall or winter...
Luggage and bags:
Unless you're visiting in May, make sure you've got your umbrella!
And bring outdoor gear. Trondheim has great surroundings for almost any kind of sports within 2-3 hours.
Clothing/Shoes/Weather Gear: Something waterproof?
Toiletries and Medical Supplies: The chemist is open 24h
Camping/Beach/Outdoor Gear: what ever you like? although there are some hills, a bicycle is nice to have