If I decide to purchase a new phone, would another person be able to use my old one (they are a Verizon Wireless customer) without any problems? Someone was telling me I might have a problem with the ESN # or something?
Once you activate your new phone, your old phone is clean and can be sold.
If your old phone was on a prepaid plan, it has to have been active for at least 6 months before it could be used on a post paid plan. If the phone was on a post paid plan, and you simply deactivated it to use a new phone, then sure, you can sell or give it to another Verizon customer to activate on their line. There should be no problems at all.
Essentially the only time they wouldn't be able to activate the phone would be in any of 3 cases. One: you lost the phone at one time or had it stolen and returned, and during the time it was gone had suspended the line due to a lost phone, and had activated another phone as a temporary replacement (its complicated but Tech support has to remove it from a list of phones that have been reported lost or stolen). Two: Your account was disconnected due to nonpayment (seeing as how you seem to be thinking of upgrading, should be no problems there ) Or 3, as Suzy pointed out, if it was a prepaid phone active for less than 6 months. ^_^