Now that most mobile phones use operating systems in a similar way to desktop computers, you are more likely to want to change your OS. Typically you can change your mobile OS to a newer version of that OS, but some phone users have had experience changing the operating system entirely, rather than just the version. Note, however, that changing to an unofficial OS will likely void your warranty.
Upgrade the BB OS if you use a BlackBerry smart phone. BlackBerry's do not accept any other type of operating system, but Research in Motion (RIM) does upgrade the OS quite significantly with each release. OS 6 is the latest version (as of February 2011) and you can download it from the main BlackBerry website.
Experiment if you have an iPhone. iPhones are typically the most closed-source mobile phones, but if you jailbreak your iPhone then you have many more possibilities. You can hack an iPhone to run Linux or early versions of Windows. This will be a complex process and will not be easy for a beginner.
Upgrade your other OS using the relevant websites. Android releases new versions of their operating system as does Windows Phone (previously Windows Mobile). Windows Phone completely redesigns the user interface from earlier versions.