Is it possible to connect two ios devices using sockets by getting their IP addressess?

There are two major problems to peer-to-peer communications: discovery, and reachability.

First, you need to know the IP address of the other peers to connect to them. Once you're connected to a mesh of peers, they can all keep each other updated on the state of the network, suggesting better peers to each other, passing around notifications of new peers who've joined and left, etc. But you have to design and implement a mechanism for trading that information. More importantly, you need to jumpstart things in some way, because when a new peer starts up, it's in a mesh of just itself, and it has no information to give itself.

One possibility is to have a handful of well-known "superpeers" (that you run) that are always connected, and bake their addresses into the app. Or you can have "introduction servers" instead of peers, serving much the same function. Or you can have some external way of trading addresses (the simplest is that users trade them on a web forum or an IRC channel or in person and type them in manually), which can be automated to various degrees. There are also shortcuts that can help—Bonjour can get other peers onto the mesh as long as one peer on the LAN is already there; GameCenter/GameKit can be used as an automated external trading network; etc.

Once you've solved the discovery problem, you still have the reachability problem. Most iOS devices usually don't have publicly-accessible IP addresses; instead, they're behind routers that do Network Address Translation, whether they be a home WiFi router or a cell carrier's 3G network. This means you need some way to do NAT Hole Punching to get two iPhones talking to each other. Somebody who knows both the public address and the internal address of each device can arrange for them to set up a connection to each other. You can have either normal peers do this (although that makes the jumpstart problem even bigger) or have your superpeers/introduction servers/etc. do it.

If you want to build all of this yourself, you probably want to look at other implementations. BitTorrent (including trackers and DHT) is well-understood and documented at a continuum of levels ranging from "lies-to-children" for curious end users to detailed protocol specs and open source implementations. And then look at some other P2P networks, because BitTorrent is not perfect, and doesn't try to do everything that everyone's come up with.

You can use GameKit. It has the matchmaking api that can help you.

It can be used for non game apps.

I've been working on something similar and it's a giant pain in the ass. There are 3 considerations: 1) Reachability 2) Discovery 3) The connection itself.

1) Don't even consider using 3g/4g, it just won't work well for keeping an open socket connection.

2) I'd use some sort of broker service between the two on the internet to connect the two. For discovery, you can just list what devices are available on the service.

3) For the connection, I find the IOS socket libraries to be rather painful to use, but if you go down to the BSD socket level it's not as bad. I think it'd be very interesting to use zmq sockets; that might simplify writing the broker service.