Yes they do, but according to some reports it's not so common any more to find the really elaborate pranks that people used to play on their friends, families and colleagues. This could be because we are more away of possible consequences; for example there was a case several years ago where a man was sent a fake memo telling him about some work he had to do. Not realising it was April Fools' Day he rushed to do it, and actually made himself very ill through stress. In our times when so many people are prepared to bring legal actions, we may be nervous of playing a trick that could lead to accusations of this kind.
However, people do still like to tease each other in small ways on this day, and the newspapers usually celebrate by printing one untrue story (for instance, many years ago the papers reported that there would be no pasta in the UK that year due to a bad spaghetti harvest!)