Heathrow Express is fantastic -- quick, quiet, smooth, and has Internet. I use it whenever I am going between LHR and north/central London.

For some parts of southern central London, however, it's just as quick to take the Picadilly Line as it is to get up to Paddington and get on the train. For example, Chelsea to LHR takes about ten minutes longer on the Heathrow Express.

Maybe I just need to use the Virgin LimoBike