I'm pretty OCD when it comes to multi-tools, general preparedness for flats, and adjustments on the fly. I carry what I need to carry so I can be self-sufficient and self-reliant. That being said,
I try to carry the least to accomplish the most.
Specifically, what do I need to do, and which tool do I need to do it?
1) Loosen through-axle to remove wheel and fix a flat... 6mm hex head
2) Adjust saddle height / fore-aft / angle... 5mm or 4mm hex head
3) Tighten miscellaneous bolts (i.e. stem bolts, top cap, bottle cage bolts, etc.) that might be loose or a bit "rattly"... 3mm / 4mm / 5mm hex head in most cases, sometimes a T25 torx head
4) Tighten pedals... 8mm hex head (in most cases)
5) Cleat adjustments... #2 phillips head
If there were a 7-function multi-tool that had 3/4/5/6/8mm hex heads, a T25 torx, and a phillips #2 with nothing else I'd be set. So far, I haven't found one

.
I find 9-function tools to offer the best balance of function and weight, so I primarily carry the
Topeak Mini-9 (92g) or the
Silca Nove (85g). They both have the same selection of tools (2 / 2.5 / 3 / 4 /5 / 6 / 8 mm hex, T25 torx, phillips #2), come with everything I need and not much I don't. That which I (mostly) don't need, which are the 2mm and 2.5mm hex heads, add almost no weight and are not totally useless.
Another tool that looks really good is
Wolf Tooth 8-Bit Pack Pliers (70g), which I don't own or carry. It has all of the same functions as the above mentioned tools, plus it can also remove and install master links.
As referenced by
cyccommute , Fix it Stix and Prestacycle are also awesome! I own both, but only carry them for very long, epic adventures.