What kind of phone are you looking to use on Verizon?
Straight Talk does have a few phones that run on Verizon, and even allows BYOD as long as it's 3G only (no LTE phones) and not an iPhone. Their iPhones run on Verizon.
Then there's Page Plus, Selectel, TalkforGood, and NextG.
Past providers: Page Plus, AT&T, T-Mobile, Virgin, Straight Talk
Past phones: Nokia 820, Motorola Atrix HD, iPhone 4S, HTC One V, iPhone 4, Nokia Lumia 900, Nokia N9, Samsung Focus, Samsung Captivate, Nokia N900, HTC 8525, iPhone 3GS, iPhone, Nokia E61i, Siemens A56...