It varies from country to country and also what you're asking of the concierge. If it's just booking restaurants, taxis and so on, a tip when you arrive is fine. If it's getting a table at an impossible-to-get-a-table at restaurant or the best seat in the booked-out-for-months-in-advance show, then you tip well when you arrive and probably again when you leave - especially if you've been using their services during your stay as well.

If you're just passing by the concierge and asking for a map or directions somewhere and not taking up more than a couple of minutes of their time, no need to tip, unless you're in the US where it seems to be mandatory.

The more effort you require of the concierge, the more difficult-to-get things they're getting for you, then the more you tip. The only exception to this might be Japan where tipping is still frowned on. In Europe, doormen and concierges do expect to get tips and can make some seriously good money.