Great way to get to Brighton or to go on an excursion if you want to save money. It's almost always cheaper to grab a coach, but it will almost always take longer too!
Most coaches in and out of Brighton are run by National Express and services to all major London airports, as well as London Victoria are available.
Typically you're looking at around 135 minutes to get to Victoria or Heathrow, 4 hours to get to Luton or Stansted Airport andaround 3 hours to get to Southampton. A couple of the routes are only worth taking sometimes - the price can be the same as a train for the journey to Victoria, if you book in advance, but the journey takes twice as long. It does save a lot of money if you're travelling at peak times though, which is worth bearing in mind.
If you're going further afield, most coaches will change at Gatwick airport, which is about 40-60minutes from Brighton by coach, or Victoria. From these you can end up on a coach to pretty much anywhere in the UK and on the longer journeys, you can save a lot of money via coach.