eppy, to have ringtones assigned to contacts, notifications, etc., you need to use a Ringtone App. Some are free, some are paid. Some are easy to use, some are a pain-in-the-a#%. Apple has a thing (like with so many "things" they like to control) where they don't just let you assign a song/sound to a Contact's (or other-type notifications) ringtone directly from your Music Library. The song/Tone has to be put into iTunes as a "Tone" via an App, then once synched to your device you can add the Tone to any Sound-related function. Most Apps have the proper instructions to do so.
I use Ringtone Designer by Blackout Labs. I use the free app and it works just fine. They have both a paid and a free one. If you search "Ringtones" in the App Store you'll get lots of choices.
Ringtones can be tricky (as we have all learned in the many topical posts on here!) on iOS devices. The clue is understanding precisely what you are buying/downloading (that is, is it REALLY a Ringtone or just a short version of a song labeled in iTunes as a Ringtone but it really isn't - stay with me ...).
Long and short of it is you really need to have a Ringtone App on your Device for MOST "Tones" downloaded - not ALL, but most.
I came across an excellent User Review in iTunes which helps explain, in detail, what I'm trying to convey and, rather than repeat or plagiarize it, I have included the link. It's for a specific Ringtone Album because I couldn't find a way to get a link to just the Review. Open the link, under the Album artwork click "View in iTunes", go to Reviews, sort by "Most Recent" and the first one that shows up (as of today anyway) is by Jenn Nichols, titled "Here's a Solution ...". The link is: http://itunes.apple.com/us/album/ringtone-hits-vol.-2/id498297546
Hope this helps clarify some of the confusion and frustration users are experiencing with Ringtones. In my experience once I downloaded a Ringtone App I could make ANY song a Ringtone or Text Tone. Some are free, some are paid, some are overly complex to use, some easier (none, though, are EASY - just the nature of iOS), but in the end you get your songs converted to Tones. Once in Tones on iTunes they can Synch to all your iOS devices as such.
That's not completely true although it is definitely an option. I personally have never used a ringtone app to create my ringtones for my iPhone and have had no issues with any of the tones I created. I simply used iTunes to edit the 20-30 sec clip of a song I already I owned (making sure it was in AAC format or converting it to such if it was not), right clicked on the created clip so that I could choose the option to locate the file in Windows Explorer (I use a windows PC so this would be different for someone using a MAC...the steps are available on the internet though), changed the file extension from m4a to m4r and clicked "ok/yes" when the warning box popped up, and then double click the file so that it will begin playing in iTunes...at which point it will automatically show in the Ringtone list in iTunes. Then simply sync the ringtone(s) to the iPhone and assign it to whatever I was trying to use it for. It's really not that hard to do although the list of steps may seem like a daunting task at first. But for some people, using an app seems like an easier way to do it so it's really about whatever makes you most comfortable.
Main rules to remember is that the clip has to be converted to an m4r to work on the iPhone, the clip needs to be around 30 secs or less (although a few of mine are over 30 secs and work fine...when you try to sync if the file is too big/long then a message will pop up telling you it could not be synced. If it does, trim it down and try again), and you have to sync it to the iPhone regardless of if you use an app or if you make it yourself using iTunes. A long time ago (probably closer to February 2011) I posted the detailed instructions I found online to help me convert the ringtones I already had in iTunes but was using for my BlackBerry which is the same process I use today...only difference is that I initially got to skip the step of actually creating the clips because I already had them.