Yes, you can, ive know a few people that have done this. There are a few version of these Visa gift cards. There are gift cards, ie 25$, 50$, 75$, 100$ (i believe there are higher ones, but havent seen them in stores). (7$? activation fee) There are also some reloadable ones, you put money on it and you use it. There are a few company, i only seen 2 of these. Safeway is the place to go if you need gift cards, they have so many gift cards...
Vanilla Visa - Works, online/phone...anywhere but only in the USA, including online purchases, u may get away with it depending on the credit card acepting thingy w/e its called. If u got this and need to buy worldwide stuff you could create 2 Paypal account and send money to your other one. Note that paypal take some % of the money and you will only be able to buy stuff online that accept paypal. The name on it was a gift for you, and when buying stuff online, my friends were really confused what name and reg address to use. Definitely alot of online problems using this company.
AllAccess/NetSpend - From what i think AllAccess and NetSpend are same company. You can buy stuff worldwide. You go online or on the phone and register your name and address and phone number on it, it can be changed later on. This company also have reloadable ones, never know anyone that tried these. (I've seen these card in some gas stations and Safeway)
Greendot - Reloadable, do not know much about this card. Ive believe it involving something like buying a card, and they send it to you in the mail, i dont know how to reload these...
There are a few other visa ones i saw that were weird, make sure when you buy them to see if they say online ok and worldwide, and not limited to a certain region. I saw some newer ones recently but do not know anyone who used them and i never tried them.
There are AMEX but they suck (not alot of place accept them, havent seen worlwide or maybe it was internet use ones) and u should not buy them, and thats off topic