Can EU citizens 'border-hop' between Schengen countries to prolong their 90-day maximum stay?

As @phoog says, yes, you can do that.

And contrary to what it seems to be at the first glance, the country you repeatedly enter may be totally fine with this: Remember that for the 90 day period in country B (unless you register) your country of residence A basically stays responsible wrt. social insurance.

E.g. if I being German with previous residence in Germany go to Italy and within the 90 day period need to go to the doctor, the German health insurance will be responsible to pay to the extent the Italian health insurance would pay if had residenza (and health insurance) there.
Of course, the German health insurance will make me pay their fees for this – and they would be in a very unpleasant category (default fee is about 800 €/month) if I didn’t register correctly with the German health insurance.

In other words, not registering may turn out to be rather more expensive than registering. This is even more if I’d then start working in Italy: I’d automatically pay taxes, including health insurance. But without registering I wouldn’t get the health insurance benefits from Italy, and without the form from the Italian health insurance saying I’m registered there, the German health insurance will not let me get out of that very expensive category and will go on sending bills (and if you don’t pay them, they won’t forget or forgive that, neither). So in case of the employment contract without registering residence, I’d pay twice.

Of course, if you move the other way round, you may get German health care for, say, the Italian taxes you still pay. Germany doesn’t care as Italy has to pay for that. However, Italy may start asking questions after a while (e.g. the tax office may have a questionnaire to determine where the “center of your life” is).

Yes, they can, indefinitely. However, the penalty for staying longer than three months without registering (not “90 days”) must be proportional to the penalty imposed upon a country’s own citizens for not registering. In particular, they cannot be deported. In most countries this is a fine; in others there’s no penalty at all. There seems to be no rule about how long an absence is required to interrupt the three-month period because it’s not particularly important to determine that except to defend against a penalty.

The controlling legislation is directive 2004/38/EC.

The freedom of movement rules are promulgated as a directive which means it is up to each member state to flesh them out in its own laws.

As such, it differs considerably between member states which registration requirements they impose on EU/EEA citizens — and where they do, they don’t have to use the same detailed criteria for when the registration requirement kicks in.

Importantly, individual citizens don’t usually get to interpret the directive by themselves — the national law is what the national law is, and to the extent that doesn’t match the directive it is up to the European Commission to (try to) force the relevant government into compliance.

It seems very unlikely that the Commission would bother to quibble about each member state’s exact rules for how to determine when a new 3-month residence period starts, unless those rules look like an attempt to circumvent the intent of the directive. All a citizen can reasonably rely on without actually researching the national law in question is that he won’t have to figure out where and how to register as long as his circumstances match the usual case where he stays for no more than three months, and then leaves and doesn’t return (other than under obviously “not actually living there” circumstances) for a long period of time compared to those three months.

In practice, a member state’s enforcement of its registration rules will not be based on border crossings specifically, but on other kinds of case-by-case evidence that the person in question has been living in the country for so long that he needs to register.

EU/EFTA countries except Switzerland

This rule is extremely flawed altogether: as Schengen countries don’t record movements between them (even when internal border checks do take place, most commonly when entering Sweden or Switzerland by bus), there’s no way to track someone’s presence in one member state vs. another.

Furthermore, an EU/Schengen citizen cannot be deported or banned from these countries unless they pose a proven health or security risk. And even if they are, keeping a Schengen citizen out of another Schengen country will be nigh impossible in practice, again because of the largely open borders.

Thus, the actual question is moot: not only is the issue not addressed in legislation with regards to EU/EFTA citizens, but even if it were it would be virtually impossible to enforce (just as with the 90/180 rule for residence permit holders).

Switzerland

For EU/EFTA citizens, a residence permit must be obtained for stays longer than 90 days within 180 days. Failure to comply with this can lead to hefty fines. Again, however, entries and exits are not recorded, even when entering/exiting Schengen through a Swiss airport, and so this is hard to enforce, although I have been subject to a raid by municipal police in my apartment complex, whereby my ID card and residence permit were briefly taken for verification.