Which iPhones don't have a sim card?

My iPhone is verizon and doesn't have a sim card. But AT&T, and a lot of other carriers do. This is only for iPhone 4

Verizon is very special - they're just about the only major worldwide operator who use the CDMA standard, which is completely different from the GSM standard. Because of this, there's no SIM card, but instead the iPhone is registered to the network by its ID instead of the SIM card.

Verizon and Sprint iPhone 4 (and earlier) don't have a SIM card. But starting with iPhone 4S, they do have it (although the SIM only works when you're outside the USA, even if you unlock the phone).

This is because Verizon and Sprint are CDMA carriers, but AT&T and T-Mobile are GSM. Only GSM uses SIM cards. Most phones outside the USA also are GSM.

The iPhone 2G, 3G & 3GS all do have SIM cards because those were GSM only models.
The iPhone 4 had a GSM & a CDMA model
The iPhone 4S was a worldphone GSM/CDMA model
The iPhone 5 is the same setup as the iPhone 4 in this regard.

So to answer:
Only the CDMA models of the iPhone 4, 4S & 5 don't have or use SIM cards.