LCD monitors

Are LCD monitors affected by speakers being too close to them in the same way CRT monitors are? Will there eventually be image distortion?

No, you should be fine

The short answer: No.

The problem with speakers and CRT monitors is that CRTs operate by electromagnetic deflection of an electron beam, and nearby magnets can distort the beam. Even worse, a magnet near a CRT monitor can cause some of the internal structures of the monitor to become magnetized, which means that the visual problems will remain even after you move the speakers away! Most modern monitors have degaussing (demagnetization) built-in, but if you really magnetize your monitor severely it might need treatment with a degaussing device.

Speakers that don't have special magnetic shielding should never be placed close to CRT monitors. Most of the speakers sold as computer speakers are shielded, and can safely be placed near a monitor. If you have a speaker set with a subwoofer module, the subwoofer is usually NOT shielded and should not be placed near the monitor; the small satellite speakers are shielded and thus are safe.

LCD monitors don't use an electron beam; nothing in their operation is affected by magnetic fields of any reasonable strength. (I reserve judgement on whether magnetic fields of UNREASONABLE strength, like the ones in MRI scanners, could have some effect.) Putting your speakers near an LCD will have no effect whatsoever on your display, either short or long term.

I don't know whether magnets have any effect on plasma displays, though I suspect not. In any case, plasma displays are all very large; if you have room for one, you will also have room to put the speakers a foot away from it! OLED displays, when and if they find their way to the computer desktop, will be immune to magnetic effects just as LCDs are. As for electronic ink displays (i.e., the Amazon Kindle or the Sony Reader), I believe they will also be safe near speakers.