You get accepted by your department first which means you are definitely given a place at a college.
After you are accepted by the department, your application passes to your first preference of college (if you gave one) and you are either accepted there, or you get passed on if there is not enough space for you. This is now allocated by random rather than the senior tutors getting a list and picking their favourites like it used to be :P
Also there is a pooling system in place. Each college belongs to a group of supposedly similar colleges. If you apply to one, but there is no space, then you get sent to another college within that pool. The exception to this is University College as receives the most applications.
Even if Durham is your insurance, you will get a place at a college and accommodation for your first year. I haven't heard of any cases where a student has had to get private accommodation, which happens at other unis.
Also, it is very difficult to change college once you have been allocated one. And tbh you will probably end up loving whichever college you end up at even if it doesn't seem that way at the beginning :P
Out of interest, which colleges did you look at on the open day?