If (and only if) there is a zero interest installment plan available, technically the only uncontrollable risk is that there will likely be a hard inquiry on your credit report which may or may not also have a corresponding debt obligation attached to it. (Personally, I recently signed up for one such plan with Google and I had a hard inquiry but no debt added to my report). The other risks are that 1) your monthly payment goes up, so if you are living on a tight budget the added payment might make it harder to meet your next bill, and 2) you could miss a payment which generally triggers interest to accrue retroactively at a high rate, and in some cases could be grounds for immediate repayment.
The pro / reward of these plans is that you have to spend less of your capital upfront, which you may be able to use for other purposes (presumably with a higher net present value than purchasing the item you're considering outright). A larger example would be purchasing a new car. You want to buy a $50k car and you have the cash on hand to pay in full, but you are being offered 0% interest for 36 months. You may be more inclined to take a loan at 0% with 0 down payment and invest your money in another vehicle (no pun intended) that offers you a decent rate of return and you will come out ahead in the end. Of course, this example works in a perfect world where you can get such an offer, there are no extra fees available, you aren't worrying about your debt-to-income ratio in preparation for a big purchase like a house, there isn't a higher insurance premium to consider, etc.
In short, 0% financing, be it for a phone or a car, can be a nice perk for the informed consumer who is not using the financing as a way to purchase outside their financial means, but it is offered by companies as a way to make people buy things they normally would not and, hopefully, capitalize on people missing payments in order to reap the sweet 20%+ interest rates generally seen with these offers.
In your specific situation with the phone, you should consider if you get a discount on your monthly plan for purchasing outright, or if you can get the phone subsidized if you sign a contract (and you know you like your provider enough to stay for its duration). If the monthly plan rate stays the same and you're looking at either $500 now or $500 over 24 months and you don't mind a hard inquiry, there's not much of compelling reason to pass on the financing and hold on to your $500.