It all really depends on the strength of the magnetic field generated by the other devices. Though even a weak field can have a cumulative effect over a long period of time.
One easy way to solve this problem would be to get an LCD monitor, which doesn't use magnets to aid in displaying images. They cost more, but do pay for themselves over time in reduced power consumption over CRTs. They take up less space too, which is always a bonus in my book.
Otherwise, your Xbox is probably fine to have nearby, but a TV and VCR operate using magnetic fields so may not be the greatest thing to have around. Unshielded speakers would depend on the power. Your typical stereo desktop speakers probably don't generate a powerful enough field to even make it to the TV, even if right next to it. The more powerful the speakers, the more you want some distance.
I'd suggest considering the LCD monitor. It's an investment, and it may take a few months to a year, but it will ultimately make you money over a CRT.
I am worried about magnetic interference with my monitor. I recently had to return my monitor back where I got it from because it was acting weird and I thought it was just the monitor's fault. I'm thinking that I was probably the cause of the monitor messing up. Is it safe to have other electronics close to your monitor? I have my xbox, tv, and vcr a few feet away from my monitor. Should I move these? (even though I have no where else to put em' really....) If that's not the problem what about non-shielded speakers? I don't know much about non-shielded speakers so how can I tell the difference between shielded and non-shielded? The only speakers I have are the ones that came with my computer and I really don't have a choice to move them that far away because the cord isn't that long.
Can someone help me with this problem please because I don't want my new monitor to suffer the same fate.