The key to success here is keeping the little animals occupied. Depending on your own personal budget, this can involve anything from simple party games and an abundance of fun children's toys to bouncy castles and magicians.
That isn't to say that a children's party has to cost the earth. Party games can be arranged with nothing but a bit of imagination and time, and fun party toys to keep them going after they've worn you out can be purchased online for next to nothing. Think about games that will help them expend some of that excess energy - anything where you can keep them moving in a controlled and fun manner will mean that they will be much less likely to have to paint your cat in icing sugar or hide jelly in your bed.
Obviously disposable cups and plates are a must - if only disposable windows and walls were an option too, then we would never need to worry - and limiting the party area will help you control the party much more easily.
Whatever your budget, the most successful parties will have catered for every eventuality. Giving every child their own individual party toys is a great start, but keeping a few choice children's toys in reserve for when all the fun and games are over may seem like a lifesaver.
Encouraging quieter games is always a great way to help them calm down if you fear a coup is brewing, but this will only work for so long. The more creative you are and the more ideas you have stockpiled for that metaphorical rainy day, the smoother the party will go. For instance, try scattering disposable cameras around the place and let the kids document the day for you. Creating a theme for the party may also ease the workload for you and give the children something to focus their wayward attention on.
Every child, and indeed parent, will be expecting a goody bag at the end of the party, and to save on tantrums, having a mix of sweets and a few more cheap little gifts is a must.
Obviously, whatever the party, the main focus is to make sure the children have a day to remember, but that doesn't mean it has to leave you on the verge of a nervous breakdown. Where possible, try and enlist help from friends or other parents to take some of the weight off your shoulders, and remember as long as you capture their imagination, they will do all the hard work for you.