As others have said, PADI members can verify certifications over the internet. Our shop has not found a way to do that with any other agency's certifications.
SSI and IANTD are pretty good about following up our fax requests, and we usually get a reply about one business day after submitting a request. Some agencys charge for this service, though I don't know whether SSI or IANTD are one of those. Of course, one business day isn't so good if you arrive at your dive destination late on Friday. You may be waiting well into Monday before your certification can be verified.
In my experience, a few agencies' records seem to be difficult to search. Replies may not come for several days if your records can be found at all.
Many agencies have problems searching their oldest certifications, so if you were certified in the 70's or earlier, it may be worthwhile to order a duplicate card while you still have your old one.
It helps if you make a clear photocopy of both sides of your c-card and store that somewhere at home where a friend could reach it and fax a copy to your dive center. The more ways you have available to verify your certification, the better off you are.
The obvious lesson is to always carry at least one c-card on your person while you travel. Having your card in your luggage doesn't help when your bags don't arrive when you do.