Effect Of Electronic Devices In Close Proximity
This is a pretty broad question... so the answer is... it depends how intense the EM field is. At one extreme, you could have a very strong EMP like the one caused by detonation of a hydrogen bomb! On the more mundane level, the EM interference that electronic devices cause to each other is commonly a concern and studied under the (obvious) name(s) of electromagnetic interference/electromagnetic compatibility. I also agree with the comments below your question that while this is a concern, whether it is the biggest... it depends on the application.

The computer components that you mention (HDD, SSD) almost certainly have been tested for both EM emissions and susceptibility (to those), so they're very unlikely to affect each other that way in close proximity. You're more likely to have issues with heat dissipation (or rather accumulation) when you pack a lot of devices like those close together. Also, (mutual) vibration is a common concern in HDD arrays; the RAID-grade HDDs will typically have some firmware features not present in desktop HDDs to better cope with that.

EDIT: As user/consumer there is one (software/firmware) bit that you can do to limit EM emissions from computing (and similar) devices: make sure your computer has enabled spread-spectrum clock generation its BIOS/firmware; it should be on by default precisely due to EMI regulatory compliance issues.

Since you (now) ask in the comment below about a cell phone affecting computer components... that's a more dicey issue. A cell radio will emit a lot more than (other) computer components... by design! It can certainly affect some critical-care electronic equipment (although almost exclusively older ICU equipment/designs) and supposedly electronics on-board airplanes (again a controversial issue; the fairly recent [2013] relaxation of FAA rules still prohibits the use of the cellular radios inside the [smart]phones, however the even more recent 2014 decision of EASA does allow the cell radio to be left on) etc. Obviously the cell phone itself (which if it's a smartphone is basically a computer with flash memory like in a SSD etc.) works well enough in the presence of its own cell radio, but I honestly don't know if typical desktop computer components get tested (by their manufacturer) for correct operation with a cell phone radio right on top of them. Maybe you should ask that as a separate question.