In my experience hostels pretty much anywhere in Europe can be full in summer if you don't have a booking.
You can start risking arriving without a booking once the weather starts to change. If you are just going to rock up at the hostel unannounced your chances are much better in the morning around check-out time.
Then again I hate booking hostels, even in high season. What I often do is this:
- Find some Wi-Fi when I arrive in a new city.
- Look up hostels on both HostelBookers and HostelWorld. Both sites can mark all the hostels in an area on a map.
- Do a Google Maps search for "hostel OR backpackers" around my current location.
With this method it's possible to see which hostels have space and also weigh up how far they are from you and check the reviews to help pick one. Making an online booking even an hour before you rock up at the door can make a big difference when a city is crazy busy.
Occasionally you can even find an online special price. I got my bed in Sofia for 5 euro this way!
But I still risk it plenty of times because I can handle it OK when hostels are full, but some people can't handle it, especially if you're not alone you don't want to start fighting over this stuff with your travel companions. And getting last-minute beds is always harder the bigger your group is.