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As Reza notes, if your switch is working fine and you don't need any newer IOS features, there's no need to upgrade, yet working fine might be qualified with at-the-moment.
Generally, to avoid tripping over known bugs, that have been corrected, you might consider upgrading to the latest image in your current software train. For example, if you had 55SE3, you might want to move to 55SE9. Usually, such an upgrade is fairly safe, but Cisco (as other vendors do too) occasionally introduces new bugs, even with just bug fix releases.
BTW, some bugs are security related, so even if everything is working fine, without an updated IOS, your device may be exposed to a known security flaw. To fix some of these, you sometimes need to jump to a newer IOS version (which exposes you to bugs also introduced with the new features).
Another reason to upgrade to a newer IOS, sometimes Cisco makes internal improvements to how the device performs. I.e. it just works a little better doing what it already does.
To recap, the biggest reasons to upgrade are to address known bugs, which are causing you issues, and/or use new features you really want to take advantage of. Either of the prior reasons sort of forces you to upgrade. However, even when you're not "forced" to upgrade, there still can be advantages to upgrading. The latter, though, can be a difficult decision because any upgrade can introduce new problem issues.
PS:
BTW, the 55SE9 image is consider by many to be about the most solid 3750 (and 3560?) IOS version.
