Can a charger not 100% compliant to the USB specification damage my Andoid phone? I've bought a world adapter which can charge USB devices as well.
According to the packing the usb will be powered with more than the 500mA as per USB specification - 1000mA.

Will charging my HTC Desire with this USB/travel adapter damage my phone?

I know that many main boards don't deliver 500mA per socket esp. when another draining device is attached to the neighboring port.
In most cases your phone will only draw as much power as it needs, and it's OK that the charger can provide more.  However, unless you know that your phone will do this and has other power management safety features, I wouldn't use the charger myself.  I've never had a phone ruined, but I have had batteries ruined by non-official chargers (including one charger that claimed to meet the specifications for my phone).