Loads of queries on this thread about which colleges receive the most applications! I looked it up for my own interest in the official Durham Uni admissions stats, and thought I'd summarise a few figures below for anyone else who might be interested.
The figures are for the 2013/14 admissions cycle (ie for entry in 2014/15, including deferred entry applications). The FIRST figure is the number of applicants who put that college down as their preference when they applied, the SECOND is the number that actually ended up in that college.
College of St Hild & St Bede: 838 / 315
Collingwood College: 1,760 / 405
George Stephenson College: 961 / 436
Grey College: 829 / 300
Hatfield College: 1,242 / 290
John Snow College: 863 / 355
Josephine Butler College: 2,000 / 259
St Aidan's College: 336 / 262
St Chad's College: 1,212 / 122
St Cuthbert's Society: 1,012 / 334
St John's College: 593 / 147
St Mary's College: 1,503 / 228
Trevelyan College: 470 / 207
University College: 3,638 / 212
Van Mildert College: 617 / 347
Remember the figures are just a very rough guide to the relative popularity of each college, NOT an indication of what percentage of applicants overall get an offer from Durham, so don't be disheartened! That figure for 2013/14 was 26,030 applications and 16,702 offers made.
And as others have said, don't forget you're actually applying to the university rather than the college per se - so if you put down Castle (University College) as your preference and the university wants you, but they don't have room for you in Castle, you'll still get an offer from another college. In other words there's no harm in putting down the college preference you'd like most!
If you want to drill down into the applications/admissions data you can go to
https://www.dur.ac.uk/ug.admissions/admindocuments/admissions2013-14/