Good quality multitool (so many are crap)
Mech hanger for a bike you sold 2 years ago
It's not so much about need, for me, it's about simple stuff that can avoid a ride being ruined. All it takes is a loose brake bolt or a snapped chain to knacker you so even if you never use this stuff for a year it's still worth it. For most of my rides I could carry nothing at all, it's always realistic to walk back but walking is less good than riding.
I've got a couple of small "nice to haves" in mine as well- a set of worn brake pads (easier to fit in the cold than a new set), a couple of common sized bolts (though mostly you can just move bolts around from less critical locations if one goes missing). A pair of latex gloves, both good for trailside spannering and saving your fingers if it's unexpectedly cold or wet, and weigh nowt of course.
Oh and a couple each of paracetemol, ibuprofen indigestion and imodium tablets because nothing improves a ride quite like the shits, and a couple of those big compeed blister plasters as they're good for patching up holes in people, can be used as tyre boots, and also fix blisters brilliantly (it only takes a wee cut or blister in the wrong place to spoil your day)
There's also a single leftover tramadol in case I ever need to walk off a mountain with a broken leg or something.
That actually sounds like a lot but all the extras there are tiny and light. So I guess what I'm really saying is, consider what the point is of minimalism. With all my extras, there's really very little reason to get rid of them.