This is a fun variation of "pass the parcel" which is suitable for even the youngest kids, and it has the advantage of not needing any prizes! You will need to supervise the dressing up carefully and make sure that all the children get a go by carefully manipulating where the music stops!
Fill a large bag or basket with dressing up clothes, old hats and scarves, odd socks and boots, etc. If you can include some joke items such as fake ears and plastic spectacles the children will enjoy the game even more.
Form the children into a circle and give the bag to the birthday child. Put some cheerful music on. While the music plays, the children pass the bag around the circle. When the music stops, whoever is holding the bag must reach in and pull out one article of clothing (make sure they choose quickly without looking!) and put it on.
If you have a large number of children, or younger children, you will enjoy the game more with two bags circulating simultaneously (and they will be lighter for the children to manage).
Adapt this for older kids or slumber parties by including some nicer accessories, which will become one of the "going away" presents - perhaps a necklace, badge or cap. Throw in a couple of booby prizes too!