The Spectrum was probably the last computer I truly understood. Not at a hardware level (too young for that, plus the Spectrum squeezes so much functionality out of the cheapest chips available at the time that it's not trivial to reverse-engineer what was going on even today), but just the software bit.
16 Kilobytes of ROM, which (with, I think, a whole KB to spare!) implemented a pretty functional BASIC environment. This was good, but still had significant limitations, especially when looking at all the cool stuff other people were doing.
At age 12 or so, I became absolute fascinated with a pretty simple thing: Spectrum programs included a 'loading screen' most of the time, which, while being loaded from tape at a leisurely 100bps or so, populated the screen top-to-bottom, left-to-right, pixels first, then (color) attributes, as per the layout of the video RAM. However, some games loaded the screen in reverse, or did not incrementally show the screen content while loading at all!
The latter problem was the easiest to solve: instead of loading directly from tape (the header of which included the base address) into video RAM, those programs would use an alternate base address, plus a small program to copy the contents afterwards. The former was way, way more tricky, and required the realization that you did not need to use the actual ROM code to load from tape, but you could disassemble/change that code, include it in your own program, and make it do whatever you want!
This realization enabled me to implement my own 'speed loader' (bumping tape I/O speeds from 100bps to, like, 111!), in addition to the usual fare of removing copy protection from programs and cheating at games by adding extra lives, removing barriers, or just fixing broken levels (waves at Jet Set Willy).
Is a Spectrum a useful computing device today? Absolutely not, and it hasn't been for over two decades or so. But that's not the point of all this nostalgia: it's the fact that it instilled a "Hackers mindset" in me and many, many others.