I agree that "it all depends". Start with the gentle approach (dishwashing soap and lukewarm water) and work your way up the chain to more harsh methods if needed.
I have had some (a Canon 100mm f3.5 lens in LTM comes to mind) where internal haze just steadfastly refused to come off in some areas of the internal lens element. I was considering using cerium oxide - a fine polish used specifically for glass surfaces (it can be found on eBay) but in the end I left it knowing that there would be some image degradation / flare when shot against the light. But then again, had I used the cerium oxide polish it would have at least removed any coating on the interior surface anyway and so would have also had some damaging effects on image quality in at least some light.
The worst haze often seems to be associated with old organic oils (I am told that Sperm Whale oil was often used early on - I don't know when it ceased) that were used on some vintage lenses to lubricate the helicoid. If this outgasses (ambient heat contributes to outgassing of course) it often tends to settle mostly on the surfaces near to the lens iris / aperture mechanism but can migrate elsewhere inside the lens too as it is in a gaseous form till it settles on something. If atmospheric humidity gets into the lens as well, this seems to make it all worse - contributing, I suspect to the permanent etching seen in some lenses which have that older lubricant type. This seems to be why lenses from Japan have a more of this problem, even on later lenses with later lubricants - they have very long, hot, humid summers! I have never read a full explanation of the exact chemical cause of this though - does the oil / moisture mix become acidic for example? Or perhaps more excessively alkaline? Or does the oil-water combination just contribute to the deposition of the mixture onto glass surfaces. I do not know. (Any thoughts someone?)
There is one other thing to consider. Some early lens glass and early coatings are known to be very soft, especially those coatings used with internal elements. Too much rubbing will quickly degrade the glass and / or coating. Moreso than with external elements where harder coatings might be used. I have had more than one lens worked on by the guy I used as a technician where he announced that he could not get all of the haze off without risking further damage to the lens. One that comes to mind was an old Leica LTM lens. But fortunately, in that case he removed enough haze that it was not really an issue when used, in 99% of the cases.
One final thought. I never use super glue in the presence of lenses. Though most super glue hardens and grips quickly it still outgasses till it fully cures (at least 24 hours). This outgassing is a problem which causes potentially strong haze on glass lens elements (and is also visible on other shiny surfaces - though there it may not matter). This is also exacerbated by ambient humidity - Super glue sets under the influence of humidity and therefore promotes hazing. Some non-outgassing, specialist forms of super glue are available, but are relatively hard to find. Super glue hazing is said to be removable by acetone but unless there is no alternative I try never to risk it without either removing glass elements first - or at least covering any glass surfaces that might be exposed to outgassing.
