I've done a couple with typing tests. The first outlined a complaint from a customer and I had to type a letter of response. The second was in two parts, first was to send a letter to3 people inviting them to a presentation evening and the second part was typing an agenda for a meeting.
I've also had an interview with a group task. They put us into 2 groups of four and gave us a plan of an office with two floors, the plan showed the desks and locations of the PC's (not enough for one each). We then had a list of people we had to seat in the office and a list of their requirements e.g.Manager - must sit near the secretarys - Receptionist - must have PC and sit near the entrance etc.
We then had to plan the office between us and then give a short presentation explaining how we had seated people and give reasons for this. I suppose they were looking for someone who joined in, gave opinions and didn't just agree with the others and not give any input.