All the followings are Verizon phones and can be used on Verizon (including voice) and Sprint (no voice) 2G/3G networks including MVNO such as PagePlus and BoostMobile.
HTC Incredible 2 and Samsung Galaxy S3: 2G and 3G on China Unicom and 2G on AT&T and T-Mobile.
HTC DNA: 3G and 4G on AT&T, in addition to above networks.
Samsung Note 2: 3G and 4G on T-Mobile, in addition to above.
Samsung S4: LTE on T-Mobile and AT&T, in addition to above.
If you have the money, S4 is the one, otherwise Incredible 2 can be found really cheap. Some Moto phones are global too but too crappy and/or locked to worth of mentioning. The Nexus 5 is too new to know its details.