For the first week in July, what is the average temperature and do I need an air conditioned room?
http://www.yr.no/place/Netherlands/North_Holland/Amsterdam/statistics.html
Just remember actual is usually hotter or colder than the "average" and humidity alters comfort levels.
I would say yes, since a memorable feature of my first visit to Amsterdam was high humidity, combined with windows that would not open very far and hostel staff who did not seem to care.
Even if it's not really hot outside, just remember most places in Europe don't have screens and if you open the windows in the summer at night in a city full of canals, you might be getting some mosquitoes feasting on you. I stayed in Bruges during the summer near a canal in a place with no A/C and woke up with a number of bites on me. No one can predict what the weather is going to be like in any given year - If it won't significantly break your budget, it's worth having if you find yourself there during a heatwave. The A/C also can help block out some of the pedestrian and traffic noise if you are not used to living in a big city.
Of course if it's hot the air conditioning is lovely. I stayed in July in a room that had a huge window that opened onto the Canal. No mosquitos and while I know it was hot while I was there I had no trouble sleeping. If you do get a place with no air, ask for a fan when you check in. They usually don't have enough for every room, so getting your request in early is a good plan. Also, it can help with noise reduction. I find thought that ear plugs work well. I use them here in NYC.
Pam
Agree with the others- weather "averages" for non-Mediterranean Europe hide quite a bit of year to year variability.
That being said, heat waves in the Netherlands are uncommon and usually do not last long. But when they do strike, they can be insufferable unless you have a refuge from the heat and humidity.
General rule for summer travel- the only place where you will almost never miss air conditioning is in the high Alps.