I know those ferrite balls on your power cables are supposed to prevent electromagnetic interference, but I still hate them. They're heavy and they screw up my cable wrapping and storage system. Do they really make a difference or can I just rip the darn things off with a pair of pliers or something?

They are intended to suppress high frequency noise that can propagate in on power, monitor, and data leads. If you remove them you may find unwanted noise in your audio or video - or someone else nearby may. No mfgr. would include them (it costs money to do so) if they served no useful purpose. If you remove them you may be OK, or you may find you need to reinstall them.- all depending you your specific applications.

I know those ferrite balls on your power cables are supposed to prevent electromagnetic interference, but I still hate them. They're heavy and they screw up my cable wrapping and storage system. Do they really make a difference or can I just rip the darn things off with a pair of pliers or something?
It is not clear whether you are talking about power mains cords (like IEC generic cables), or low-voltage leads (as from a wall-wart, etc.)?
If you are talking about generic IEC power cords, just throw the inconvenient ones in a box and use a generic one without the filters.
If you are talking about low-voltage leads from external power supplies, that is a different matter. Typically, you can't simply remove the filter lumps. Aid it wouldn't be advisable, either. Gear with external power supplies are more vulnerable to interference entering through the power lead.

No mfgr. would include them (it costs money to do so) if they served no useful purpose.
Well, in most cases, they are REQUIRED by government regulatory authorities. As you say, probably more often than not, they add no discernible value. But I've been in situations where you couldn't live without them.

I think the key feature is that the manufacturers stick them on to ensure they can label the product as EM compliant, but the size means they're rarely that effective. You can buy them to retro fit, so why not chop it off, test it, and if you get induced hums and buzzes, replace it with a new one!