After all those posts about cake decoration, I took a class, and our wonderful instructor had a tip for this. Buy some cheap non-slip shelf liner (the rubbery kind, like rubbermaid) and put it underneath the cardboard round the cake is on. Glue the cake to the cardboard/foil/doily with a bit of icing, and you've got a secure, ready to travel cake.
The shelf liner is also a good way to lift and manuever the cake around, if you cut a bigger piece. I've been using the shelf liner under my mixing bowls and everywhere else to prevent slips.
Great tip! This should even work for transporting cakes in the car. I usually use a damp towel between the car and the tray or plate that the cake is on so that it is not sliding all over the car seat or floor. I'll have to try this method. I love those non-slip liners. I use them on the counter when I am mixing or chopping things. Now I've got another use for them!