The long and short answer to this is : NO.
Lemme explain to you why.
The PS2 was designed with three things in mind. To :
1.) Run it's own software
2.) Run the PS1's software
3.) Run DVD movies
To run XBox games, someone would need to develop SOFTWARE that would run on a PS2 that would allow it to EMULATE the XBox's system.
Now, it's really not that simple. Emulators take a lot of hard work to make, and usually require coding to be done fully in the Assembly programming language. (Imagine someone sitting at a computer, literally coding in 1s and 0s. This is the only thing harder to do than to actually program in ASM)
You'll see that there are only two emulators available there. One of them only runs Halo (at ridiculously low speeds) and the other runs at about a couple frames faster, at best.
That's it, there is no more when it comes to emulators. When people say "Oh, but I heard about this underground emulator that perfectly plays xbox games" or "My hacker/genius friend (or friend's friend) coded an emulator and it's perfect," they're referring to emulators that don't exist.
If they did, they would be listed on Zophar. Zophar is the biggest emulation site on the net, has been for a very long time, and will probably continue to be until people stop making emulators.
Anyways, to get back on topic. The only way to EVER play XBox games on a PS2 would be make an emulator that will run on it. And if you go to that link, there aren't any emulators that can even run decently on COMPUTERS. Why in the hell would there be a PS2 emulator that would? Before you can contest this, most people don't understand that programming for consoles is infinitely harder than coding for computers.
To you people who program : The biggest difference between programming on consoles, and programming on computers, is that you have to think in BITS. If you go back to beginning programming class, you'll remember that you always talked about everything in BYTES. It basically means that you have to make a math conversion for every single variable. Not only that, but every system has its quirks, quirks that are hardcoded, and usually require some sort of hack or workaround in the case that you run into problems.
Not only that, but coding on a console usually requires you to learn some very ugly APIs. Hell, the entire system's hardware specs is a friggin API.
If you relate programming to carpentry, you can think of it like this : Normal programming is like making a chair that anyone can use, console programming is like making a chair for only ONE person to ever use.
So, Person, you can plainly see :
There's no way to play XBox games on PS2. There MIGHT be in the future, but it's probably not likely. Seeing as no one's even CARED about emulating XBox on PC, it's probably an amazingly long way from ever making it to the PS2.
So, if you want your XBox games on your PS2, the only option for you is to see if the games are also on the PS2. (Most big titles are. But I can only find Outrun 2 for PS2 as a japanese version. It sucks, I can get that game for 5 dollars for an Xbox because nobody wants it, but I have to shell out 40 dollars for a japanese original for PS2)
