AFAIK when people talk about modern bikes being less maintainable, what they mean is that there's been sort of a proliferation of more proprietary parts (especially headsets and bottom brackets) in the last decade or so, along with a Gillette-razor-style arms race of increasing numbers of rear sprockets (with correspondingly narrower/more delicate chains). Frankly, it's probably not that big a deal: you just have to get the right kind of tools to deal with the kind of parts you have, and replacements might be a little more expensive than if they were more standardized.

However, if you really want maximum ease of maintenance -- or especially if you're going to be, say, doing bicycle touring in some developing country where it's hard to get fancy parts -- IMO you can't go wrong with a plain old threaded square-taper bottom bracket (don't go so old-school that you end up with ashtabula, though), cup-and-cone threaded headset, 26" wheels, and a rear freewheel or cassette* with 8 sprockets or fewer (so you can use "normal" chains). Basically, all the stuff you'd find on an old '90s mountain bike.

(* I should probably have an opinion about freewheels vs. cassettes to go along with the rest of the opinions, but I don't know enough.)