Dropbox is compliant with the Data Protection Act, the main worry is point 8 of the Act:
Personal data shall not be transferred to a country or territory
outside the European Economic Area unless that country or territory
ensures an adequate level of protection for the rights and freedoms of
data subjects in relation to the processing of personal data.
If a company is outside the EU and in the USA then there is a 'Safe Harbor' list maintained of companies that fulfil the the level of protection clause.
Here's a blog post from Dropbox saying they are now Safe Harbor certified and a link to the Safe Harbor site so you can check for yourself, might also be worth checking for other companies you're considering.
Dropbox Blog: http://blog.dropbox.com/?p=972
Safe Harbor List: http://safeharbor.export.gov/list.aspx