Always, unless I'm exhausted, carrying excessive luggage, or am injured. Or, in some cases, where there's no alternative but to get a taxi. Most of my business is in European urban centres, though, so that's pretty rare.
I've used public transport for airport and office transport in London (well, I do live there), Glasgow, Paris, Amsterdam, Brussels, Frankfurt, Munich, Warsaw, Budapest, Prague, Bratislava, Vienna, Barcelona, New York City, Chicago, and many other places (that aren't really worth mentioning through their obscurity). In fact, in most, it's far quicker (and dead easy) for getting to/from the office. In many, particularly if you're arriving at peak hours, it's far quicker from the airport too.
The money isn't usually an issue, as I could claim it back, whatever I do. However, I do object to paying in excess of £50 for some airport transfers, where it's just unnecessary. I have more of an issue with excessive use of private transport in cities, though. I would never choose to drive in London, and support the congestion charging scheme wholeheartedly (if anything, I'd like to see it go far further, with much greater pedestrianisation). If this is my attitude in London, then it would be hypocritical of me not to use the excellent public transport on offer when I am a guest in another city.