My iPhone says "No Service" even when I insert my SIM card

Of course you should talk with your carrier to make sure that SIM is correct for your account and that your account is still active and provisioned. If the SIM works correctly in other phones, then Redstone_Chef's reply may well be correct. Or your iPhone may be locked to a different carrier, if you just got it recently and this is the first time you've tried to use it.

Regards.

Your Sim Card reader is most like at the End of it's Life. Most phones are really only meant to swap out a sim once every 2-3 years, so really they're designed to handle about 3-6 reinserts. If you're doing more than this it can shorten the life and cause it to break faster. It could also be a number a things, usually battery is the main cause from overheating and warping the sim card reader rather then reinserts.