If travelling off peak, the cheapest way to make this journey is to use the Piccadilly Line, but tapping out and immediately back in at Hatton Cross. This ensures the appropriate off peak rate is charged, and the Heathrow 'tax' is avoided.
For my journey from King's Cross to Heathrow, this would provide an overall journey time of around 60 to 70 minutes but I'd allow more time than that. If I have time, and am making a single journey off peak, I am likely to use this method.
If I am making a return journey then I would be much more likely to buy a Network Railcard discounted Anytime Return from Paddington to Heathrow Rail, plus PAYG between King's Cross & Paddington, especially if I am using Terminal 5. From King's Cross, this only costs me about £1.50 each way extra to use Heathrow Express, compared to Crossrail's through fare.
I am very reluctant to pay the Crossrail tax; either I will pay more to use HEX or I will use the Piccadilly Line, depending on the exact circumstances. However if I really wanted to use Crossrail, then I would consider tapping out and back in at Hayes & Harlington; this would reduce the fare from £13.30 to £10.40.
As others have said, if making other journeys in London (or are travelling from the other side of London) a Travelcard can be well worth considering. For journeys beyond London, an outboundary Travelcard (where available) is well worth considering; these are generally avaliable for journeys made within the (former) Network (SouthEast) area.