There are tools that simply can't be substituted for generics. These really must be either purchased, borrowed, or if you're lucky to have a cycling cooperative near you then they will have tools to use.
I'd not mess around - I'd buy the right tool, but only at the time I need it.
- Spoke nipple key - its too easy to round off nipples with a spanner, and also pliers don't sit flat.
- Chain tool - If I had to put a pin out AND I needed to reuse the chain, then a chain tool is the only thing that works. If you just need to remove a worn-out chain then boltcutters are fine. Use quicklinks in the future.
- Cassette lockring tool, or freewheel removal tool. Nothing else works for this task - there is no substitute. 90% of freewheels use one tool, an 99% of cassettes use one tool. If you have something else, you will need that tool.
- Cone spanners - while normal spanners/wrenches will generally work if you can get them in there, cone spanners are much thinner and work really well.
- Pedal spanner - again if your pedal flats are too narrow for an 8" spanner, then you will need either a smaller spanner with insufficient leverage or a proper pedal spanner. Check if your pedals have hex sockets on the inside.
- Cable cutters - Doing re-cabling is much better if you have the right bypass loppers for cutting cable inner and outers. That said, a small grinder can also do this job should you have one.
Generic tools that make it easier would include quality hex tools in metric (depends how old your bike is, you may need imperial) and some suitably sized combination spanners in 6mm, 8mm, 10mm. A JIS screwdriver can be useful for derailleurs because a common philips is a subtly different shape and will damage the screw eventually.
A common threadded headset can be taken apart with a big spanner/wrench large enough to go over the flats. I have a 12"(300mm) spanner that gets this job done. If you have threadless then that's a hex tool in 5mm or 6mm. If you wish to remove bearing races, then again you will need a brass drift, a soft hammer, and patience. To reinstall bearing cups you'll probably need a press, which can be fabricated from threadded rod (allthread) and some suitable nuts and washers.
So if you have to replace your pedals, you might get away with a generic hex tool or a spanner/wrench/crescent, but if it doesn't work then you can choose to obtain the tool, either by purchase or borrowing.
Buy the tool when/if you need it.
The other option is to look out for a cheap combo tool set - they can cover the basics well enough, and when a tool breaks you've used it enough to justify purchasing the good tool. That's how I ended up buying park nipple spanners and chain tool, but still have rubbishy pot-metal grade bottom bracket tools that don't fit my bikes.