I'll contradict jakartaresident by adding another vote for Silverbird. My hotel rates in Jakarta generally include one-way airport transfer and they just book Silverbird for that. When it's included in the rate, I'm happy for them to pay but I agree with TJQuill's comment that it's better to deal direct with the taxi rather than via the hotel. The hotels I've stayed at recently (JW Marriott and Ritz Carlton, both in Mega Kuningan) usually have a few Silverbird taxis waiting outside so I just get those to the airport on the meter.

When I was last in Jakarta, Bluebird group ran an advert in the Jakarta Post explaining how to identify their taxis. Apparently other taxi firms are trading off the fact that foreigners generally like Bluebird taxis and are designing their logos to look like the Bluebird logo. I was surprised to see that there are quite a few 'regular' taxi firms that are all part of the Bluebird group but don't go under the Bluebird (or xxxbird) name. Unfortunately I can't remember what name they do go under so I still just look for the Bluebird logo!