I\'ve heard a few people say that you should never expose your internal ids to the outside world (for instance an auto_increment\'ng primary key).
Some suggest hav
As with many security-related issues, it's a subtle answer - kolossus gives a good overview.
It helps to understand how an attacker might go about compromising your API, and how many security breaches occur.
Most security breaches are caused by bugs or oversights, and attackers look for those. An attacker who is trying to compromise your API will firstly try to collect information about it - as it's an API, presumably you publish detailed usage documentation. An attacker will use this document, and try lots of different ways to make your site crash (and thereby expose more information, if he's lucky), or react in ways you didn't anticipate.
You have to assume the attacker has lots of time, and will script their attack to try every single avenue - like a burglar with infinite time, who goes around your house trying every door and window, with a lock pick that learns from every attempt.
So, if your API exposes a method like getUserInfo(userid), and userID is an integer, the attacker will write a script to iterate from 0 upwards to find out how many users you have. They'll try negative numbers, and max(INT) + 1. Your application could leak information in all those cases, and - if the developer forgot to handle certain errors - may expose more data than you intended.
If your API includes logic to restrict access to certain data - e.g. you're allowed to execute getUserInfo for users in your friend list - the attacker may get lucky with some numbers because of a bug or an oversight, and he'll know that the info he is getting relates to a valid user, so they can build up a model of the way your application is designed. It's the equivalent of a burglar knowing that all your locks come from a single manufacturer, so they only need to bring that lock pick.
By itself, this may be of no advantage to the attacker - but it makes their life a tiny bit easier.
Given the effort of using UUIDs or another meaningless identifier, it's probably worth making things harder for the attacker. It's not the most important consideration, of course - it probably doesn't make the top 5 things you should do to protect your API from attackers - but it helps.