If you still have the device (in the case of a damage claim)
Settings.. You can find the IMEI in your device's Settings app. For an iPhone, navigate to Settings > General > About. For Android, navigate to Settings > About phone > Status.
On the device itself.. This number is often written on the back of the device near the bottom , on the SIM card tray, or under the battery.
If you no longer have the device
Packaging. The IMEI of the device can be found on the box in which the device was packaged. Look for the barcode on the box and you should see the IMEI clearly labelled here.
Google Dashboard (Android only). You can access Google by visiting www.google.com/settings/dashboard and look for your device.