A list or rule? Sure, anything that uses electro-magnetism to function could, and would be affected by magnets. The question is what the detrimental effects, if any, would be and how strong and close do the magnets need to be. Generally the two most questioned items are the monitor and disk drives.
LCD/LED monitors are not generally susceptible to magnetic interference like CRTs are because they function completely differently (remember, CRTs use magnets to deflect the electron beam, so an external magnet would obviously mess with that).
Hard-drives are also not affected by magnets because of the way they function. You can research the details on how hard-drives work for a more thorough understanding, but the easy answer is that there is a very powerful magnet inside each hard-drive that controls the read-write head’s movement. That’s why some people like to rip open dead drives to get at the sweet, gooey super-strong magnet inside. If that magnet that is inside the drive, and right beside the platters doesn’t wipe them, then any magnet that you are likely to have around isn’t going to.
As for flash drives, they are a different technology altogether so they are not going to get erased.
There is one component however that is indeed affected by magnets that most people miss: cables. While many cables are shielded, some are not and thus susceptible to a magnetic field. For example, a cable connecting the sound card to the speaker may be shielded, but the little cable connecting the CD/DVD drive to the sound card usually isn’t and ingress of a magnetic field could cause interference. Or, while rounded IDE cables (especially for IDE133) are usually shielded, ribbons usually aren’t and even at speeds of 66/100 could be affected enough to cause some corruption or at least reduce performance due to re-tried reads/writes.
I would say that modern systems are not really vulnerable anymore because as time progresses, science and knowledge advances, but unfortunately that’s not sufficient. While that may be true, in the old days things were done right a lot more than today with all the cut corners and cost-reducing measures (eg NVIDIA’s “Bumpgate”).
Anyway, the point is that when it comes to modern computers (I’m counting floppy disks as not-modern), you don’t really need to worry about magnets. You can breath a sigh of relief. :)