New York: Cingular and T-Mobile for GSM; Verizon and Sprint for CDMA; Nextel for iDen. Since Airtel is part of Bharti, which is a GSM carrier, you can ignore Verizon, Sprint and Nextel. The carriers in New York are Cingular and T-Mobile.
Bangkok has several GSM carriers; AIS and Orange have EDGE services. AIS worked well for me there.
Hong Kong also has several carriers; 3, CSL and PCCW wireless are a few - there are others.
Bogota - Colombia Movil SA, Comunicacion Celular SA Comcel SA and Movistar all offer mobile services; one or more offers BlackBerry coverage. http://www.gsmworld.com
has a lot of information.