As a fun example, I worked on a safety-critical system where accessing all-bits-zero pointers would trigger an IRQ that jumped back to PC + 4, leaving the register/variable uninitialized. Great fun was had any time there was LR corruption and CPU started executing whatever happened to be next in memory after function return.
I recently had a less wild but similarly baffling experience on an embedded-but-not-small device. Address 0 was actually a valid address. We were getting a HardFault because a device driver was dereferencing a pointer to an invalid but not-null address. Working backwards, I found that it was getting that invalid address not from 0x0 but rather from 0xC… because the pointer was stored in the third field of a struct and our pointer to that struct was null.
foo->bar->baz->zap
Foo = 0, &bar = 0xC, baz = invalid address, *baz to get zap is what blew up.