A black cab will cost around £45-50 into the centre of town, plus tip. This really is about the most uneconomical way to get into the centre of London.
The Heathrow Express + cab option works out at about £35. Others seem to like this option; I dislike having to lug my bags through two stations. Seems too much like hard work.
Tube option is the cheapest, and can be nearly as quick as a car if you're headed somewhere along the Piccadilly line. When I travel from my office (Green Park) to Heathrow, the Tube is nearly as quick as a cab (about 45 minutes) and much cheaper.
Final option is a minicab, which is my preferred option to-and-from Heathrow. I prefer
Addison Lee. I normally ring them when I arrive, and they have a car and driver waiting for me when I exit the baggage claim. They charge by the mile (£1.60 per mile when I last checked) based on the GPS route, although they do charge a £7.50 "meet and greet" fee for airport pickups which covers parking charges and 30 minutes of waiting time. You can pre-book these cars to meet your flight, although I find calling from arrivals is enough notice to get a cab. Addision Lee charge about £40 into the centre of London (including tip and meet-and-greet fee) -- the return journey to the airport will only cost you £32.
One further option is to try a local minicab firm -- they tend to leave their cards on the payphones at Heathrow. On the upside, this is the cheapest car service you'll find -- typically £20-25 into central London. On the downside, the cars are often tatty, the drivers are occasionally uninsured, speak limited English, and have a rudimentary knowledge of London geography.
You pays your money, you makes your choice...