We all grew up with the rhyme - 'All work and no play makes Jack a dull boy', which tells us the importance of relaxing even at work. It also means, there's no need to be too intense about the work that we do and most importantly, we should not overlook the need to unwind occasionally.
Fun at work is an important aspect of today's workplace where optimization is the rule. Depending on what work you do, there are different fun activities that can make your work less mundane and even recharge you. One very easy fun activity that you can see in most offices is Dumb Charades and the other is Antakshari although not everyone in the office likes these activities. So, an enterprising team leader would have to find other options as well.
One nice idea is a group discussion on any topic from current events, cricket, Bollywood, etc. but the team leader will have to take charge as a moderator or else there's a chance that the group discussion might degenerate into a fiasco. This is actually a very good fun activity in the workplace because every week new topics can be introduced and participants can freely share their opinion on these topics. Friday evening movies are a great way to look forward to the weekend but it should be conditional - not at the cost of pending work.
It's not a good idea to impose a fun activity on those who are not interested in those activities. It's always preferable to have some spectators for any fun activity at work. An innovative team leader will try to understand every team member's likes and dislikes as well as comfort levels and tailor the fun activities accordingly. For instance, there might be a few individuals who are good at stand up comedy while some others may be good at writing poems. Similarly, there may be others who are good at short plays or skits.