There is a confusing variety of greases for various bike parts out there. I wonder if I can just disregard that and use a 'one-size-fits-all' grease (if such a grease exists?
Some greases really are special. But in other cases the grease doesn't really matter. Since so many companies just say to use their approved grease, it can be hard to tell apart which applications are really special and which ones don't really matter.
There are some applications where you should only use the approved grease and using the wrong grease really will cause a problem. This includes roller brake grease. This is critical to use the exact grease specified, and unsafe to substitute anything else.
Also, some frame couplers specify special fluoro-compound grease, and it's best to follow the instructions or potentially ruin your frame from thread galling.
Any carbon parts like carbon seatposts should use grease recommended by the manufacturer or for the application.
Internal gear hubs usually use oil, but it's important to use the correct lubricant. Some hubs like the NuVinci hub literally are designed around the special oil they use. For other hub types, the grease doesn't usually matter.
On the other hand there are a lot of applications where the grease doesn't matter that much. In that case I use boat trailer bearing grease, or if something lighter or cleaner is needed, white lithium grease. These include things like most steel threads including pedal threads, steel seatposts and quill stems, brake pivots, wheel and headset bearings, crank splines, cassette splines, etc.
BetterSense's answer covers many of the cases where you need a specific type of grease quite thoroughly; however, 'marine grease' is the most general-purpose grease that I've seen recommended for use on miscellaneous bicycle components (e.g. greasing a non-CF seatpost, bottom bracket work, headset greasing, repacking bearings, etc). I primarily do mountain biking; in road biking disciplines, there may be more specific greases for areas like the bottom bracket.
Anecdotally, the Park Tools general purpose grease that a friend of mine has appeared to perform nearly identical to the tub of generic marine grease that I have in my garage.
Here are the lubricants sold by Shimano:
Hydraulic mineral oil - this is for disc brakes, and is different from DOT fluid. Anecdotally people use mineral oil including baby oil, and it 'works'. But Shimano claim that only theirs is good and others can destroy your brakes. https://bikerumor.com/2013/04/11/tech-speak-brake-fluid-break-down-and-implications-for-road-disc-updated/ Take this with a pinch of salt as there are bunch of hydraulic mineral oils sold specifically for bicycles and no complaints. Different hydraulic mineral oils do have different boiling points, and different viscosity.
Internal hub maintenance oil and SG-S700 oil. These serve a similar function in lubricating the internals of Shimano hub gears, but different designs seem to warrant tow different oils. Other IGH will require oil as well, e.g. Rohloff oil
Internal hub grease. This is with calcium hydroxide 5-10%, white solid lubricants 2-3.5%, & 2.5-4.1% bentonite, other additives and mineral oil. This grease is calcium-based for wash-resistance, and temperatures are not high.
Shadow+ RD grease. This is a specific grease for Shimano's clutch for their RDs. Lubricating these is required at regular intervals. This grease is 50-60% synthetic oil, 25-35% calcium sulphonate thickener, 10-20% additives, 5-15% mineral oil. Shimano says 'Twice as durable as Internal Hub Grease, which is also for SHIMANO SHADOW RD+ stabilizer. ' The clutches on RDs create a maintenance issue for the owner, and you could use anything, but it seems that the Shadow+ RD grease was introduced because of warranty claims on the clutch derailleurs - if you used a grease with inferior wash-out properties, such as the IGH grease, or something even worse than that then providing you regularly re-lubricate it then things will be just fine. If you rely on infrequent dealer maintenance, your clutch may be running dry. So higher performance greases, just as with cars, reduce maintenance intervals.
Roller brake grease. https://si.shimano.com/api/publish/storage/static/sds/en/pdf/roller%20brake%20grease-202008-ENG-GHS.pdf This is 70-80% synthetic oil, 5-10% MoS2, 1-5% talc, 1-5% propylene carbonate (PPC), 5-15% bentonite, <1% quartz. MoS2 ('moly) has very superior friction properties for sliding surfaces. Bentonite is the the thickener (compare with lithium 'soap grease', the standard thickener). Bentonite makes for very good melt resistance. Talc is a friction reducer. I believe the PPC is also thickening. You could substitute a similar grease rather than the manufacturer's, but clearly a generic grease that doesn't contain MoS2, is soap-based, etc. would be a bad substitute.
'Premium grease' aka 'Dura-Ace' grease. This is a slightly mysterious substance, but a lot of people say it is 'similar to' or 'the same as' Motorex Bike Grease 2000. This has an NLGI of 2, which means 'normal' grease (thicker than 'soft', runnier than 'firm'). Motorex say '. Ideal for lubricating bearings, wheel bearings, joints and headset. Neutral to elastomers and seals and prevents galvanic corrosion.'. This is Ca-12-OH based, so like some of the previous greases, wash-out resistant and not a high temperature grease (rated to 120C). A lot of the time Shimano don't bother recommending a specific grease, but when they do, this one tends to be the one. Since this is essentially a generic grease, it doesn't seem like one you need to buy in a tiny pot for high prices, but you would want similar properties, most notably water resistance.
'Bike Grease'. This is another version of the previous product, and likely the same or similar.
Cable grease - this is synthetic silicone-based oil with PTFE (Teflon), and lithium soap thickener. The obvious comparator here would be a dry chain lube, however silicone washes out easier, whereas a chain lube would tend to be mineral oil based. Petroleum products can damage plastics and rubbers, and a wet chain oil would attract too much dirt.
Anti-seize - this is a soap-based aluminium complex grease with high solids. It's to stop corrosion/seizing on threaded parts, and specifically where two different metals are in contact (stainless vs steel does not count as different, aluminium vs steel does). It's not used for moving parts. If your parts are regularly maintained you don't really need it.
Freehub grease - this is sold with the note 'Hard to solidify under low temperature'. The datasheet is not too specific, but it's 50/50 synthetic and mineral oil, plus lithium soap and additives. It is recommended for some Shimano freehub bodies. Using 'premium grease' on freehub pawls is a bad idea because it's too thick and can inhibit pawl engagement. You need a thinner grease here.
Free hub seal grease . This is not for freehubs in general but is specifically for Shimano's Microspline seals, and for specific seals there. The datasheet gives the same basic constituents as the previous one, but it might be different.
The manual provides
'• When assembling the freewheel body unit, do not apply grease or oil outside of the designated areas. This may cause the freewheel body unit to malfunction. • Do not wash the freewheel body unit. The internal grease may flow out and cause the freewheel body unit to malfunction.'
Beside this forks often contain a renewable oil, which will be somewhat similar to oil used inside hubs, and manufacturers also will specify a fork lube.
The common recommendation is Slickoleum, which anhydrous calcium-soap based with good washout properties, and which is slightly thinner than many greases (ALGI 1.5) http://slickoleum.com/specifications.html
Another grease-based product is carbon assembly compound, which typically is grease + silica, which adds friction to enable parts to grip with a lower torque. This is used with carbon fibre parts, which if over-torqued can fracture.
Besides these other manufacturers sell different greases for the same job, often with different compounds. Different criteria will include:
- corrosion resistance
Unfortunately it's not very clear which grease and additives is best, because bicycles are different from lots of other applications in that speeds are quite low, and temperatures not too high. Durability is likely to be important.
Excluding the different specific functions where you need oil, rather than grease, then you don't necessarily 'need' any more than one grease. You could put Slickoleum inside your freehub, for example, or on your bolt threads, or lubricate your fork with 'bike grease'. And you can probably buy a generic grease made for mining, marine use, or whatever, that is more water-resistant than any bike grease. But different greases will do their jobs better than others, and for some jobs there's likely to be more difference between a good grease and a bad one, e.g., inside a hub (where you'd like to avoid excessively regular servicing), rather than, say, bottle cage bolts.