Generally, anyone who processes personal data needs to comply with data protection laws. 'Processing' is any use of personal data (other than for personal reasons) and includes obtaining, storing and retrieving personal data. Read Processing personal data for more information.
This means that businesses and private individuals alike will need to comply with data protection laws where they process personal data belonging to ‘data subjects’ (ie natural persons from whom or about whom they collect information). For example, an online business may collect personal data about its customers (ie the people buying its products) and its staff. On the other hand, a private individual may collect personal data where they run a blog (eg by collecting users’ names and email addresses through a blog contact form).