Heathrow: The Heathrow Express (www.heathrowexpress.com) is a regular and quick shuttle service into Paddington Station, and at £13 is fairly reasonable. If you are travelling in a group of four or more, however, you may find that a taxi will be a more reasonable option. Travelling by tube is a cheap alternative, but with current disruption to the service (until work on the new terminal is finished in September 2006) it may prove far from cheerful.
Gatwick: Two services run directly from Gatwick into the centre of London. The Gatwick Express is a non-stop train into Victoria Station, taking only 30 minutes. Unfortunately at £20 for a single ticket the cost is fairly high. Check the website (www.gatwickexpress.co.uk) for various reductions and offers. Cheaper but slower is the Thameslink service which takes 50 minutes to reach King's Cross Station.
Stansted: Because Stansted is well beyond the outskirts of London, the train is the most sensible option for anyone with more sense than money. The Stansted Express is a regular service running direct to Liverpool Street in 45 minutes. See www.stanstedexpress.com for fares.