Much of the following comes from A Chronology of State Medicine, Public Health, Welfare and Related Services in Britain: 1066 - 1999 (no longer available?) with a few minor corrections and additions.
In Scotland the official schoolmaster or other fit person was responsible for the census locally. Ancestry has a complete index. Scotlands People also has a copy of the originals as well as an index. Both are only available under subsription, but a free copy of some counties is available at FreeCEN. The information is similar to that in the England and Wales census - occupations are often abbreviated - HLW means Hand Loom Weaver for example.
An Irish census was also held. The information supplied was name, age, occupation, relationship to the head of the household, date of marriage, literacy, absent family members and family members who died since 1831. Only one set of original returns survived 1922, that for the parish of Killeshandra in Co. Cavan. There are, however, a number of transcripts of the original returns because the returns from 1841 & 1851 were used in the twentieth century as proof of age when the Old Age Pension was introduced.
There were also censuses held in the Channel Islands and the Isle of Man at the same time as the English census - these are also availaible online.
An Irish census was also held - most of the surviving returns relate to parishes in Co. Antrim.