reservations as I go

It's a tradeoff. What you can't predict is how long it will take you to find acceptable lodging in each place. It also depends on where you're going. But some people really like to travel that way. Happy travels.

Since it's still high season you might not be able to find too many inexpensive places with rooms available. You may want to solidify your schedule more in order to make some reservations. Donna

The rush is off by mid September when compared to summer. Will not be as light as November or January but certainly not high season. You will be fine if you have a little flexibility. The local TI can be very helpful.

It depends on where you will be visiting. September/October is actually high season in the big thee: Venice, Florence and Rome. It's the perfect weather, warm but not hot and the kids are back in school.

Are you going to be having a car ? I think for me that is key if I just want to wing it (which I usually do) If I can't find a place I can just drive on to where I can. This does not work however if you are doing the big cities, so when that is involved I plan a bit more, but if I am wandering Provence or Tuscany or Romania, or most of Germany I can always count on finding something, somewhere.... Where are you traveling to?
If I am on the train I do not want to find myself wandering a city with my bags and trying to find someplace...been there, done that and I don't like that much uncertainty without a car.

If you are looking for single rooms, it's hard because there aren't many. My first trip to Italy - Milan, Venice, Florence, CT. I started looking for budget accomodations about 2.5 months in advance and had a hard time.

I love the spontaneity and adventure of travel, but it does require a little more effort. You blow into town not knowing what's ahead of you, and if you're packed light and carrying everything on your back, you're able to wander around, take your time, and find a little place to stay. You gotta love it! However those cheap lil rooms are getting harder to find. I've found it's easier and cheaper to book ahead of time. There are bargains all over, even in Florence, Venice, & Rome. The internet is full of good deals. But on foot, you may have to do alot of walkin' to find them.
If you're going without reservations, make sure to do your homework ahead of time, with a good list of where these bargain rooms can be located.

Personally, I prefer being able to do some research online ahead of time so I can pick lodging based on that, rather than waiting till I get there and picking a room just on how it looks and how tired I am from traveling that day. It's all a matter of personal preference and how much risk you're willing to accept.