As many have pointed out, the whole discussion of the Paladin has several facets that need to be taken and discussed separately to form a cohesive "whole". The 2nd edition Paladin book and the 3e Book of Exalted Deeds did a decent job of addressing some of the issues in this discussion within the context of moral code and alignment respectively.
In the 2e Paladin book, it gave guidelines for players to define their moral code based on Virtues, and what powers or institutions the Paladin followed. For example, the Paladin could serve a Church, a Philosophy, a Government or a combination of the three (but not all 3 as Philosophy and Church were considered incompatible). As a Forgotten Realms DM, I could use the example of a Paladin that serves the ideals of the (decidedly lawful good) government of Cormyr, Tethyr or the Lord's Alliance; or one of the Churches of those gods that sponsored Paladins (gods of LN, LG, or NG alignments). Philosophy wasn't particularly detailed in that setting, but the closest would be the "Adama" in the Shining South but that philosophy was somewhat propped up by a combination of deities without followers praying to them specifically but rather living along the lines or interpretation of that moral code. Or one could default to "chivalry".
Suggestions for roleplaying involved conflicts of interest between between your demands to one or the other institutions. You had (usually minor, depending on kit) benefits for being a Paladin of a particular order or serving multiple patrons. Say in the example above, the Cormyrean authorities would be more welcoming or grant the Paladin a certain authority within their jurisdiction while the local temple of Tyr could offer lodging to the Paladin. On the other hand, conflicts could arise where the interests of the Church of Tyr and the government of Cormyr might be at odds. For example, the local lord commands you to report the activities of the Church of Tyr as he suspects there might be agents of some dark god trying to infiltrate it or vice-versa. Do you take the local lord's word at face value? Do you betray the trust of the Ecclesiastic hierarchy to serve the government? Etc...
The easy choice would be to eschew both and refuse to put yourself in a position between both parties which is ultimately either a "neutral" act or even a chaotic one if your motivation is to avoid risking powers granted to you, and possibly an "evil" act for refusing to investigate an allegation of wrong-doing or evil as the Paladin's role is to combat Evil wherever it lurks.
The next degree of choice is agreeing to one or the other side without moral consideration. I.e. you just go along with it. Although not quite as easy as being passive, it is the "lawful stupid" behaviour some have referred to. You allow others to make the decision for you.
The final degree of choice is to investigate both parties to see if the local lord is indeed "on the level" but also check to see if his suspicions are correct. Based on your observations YOU make the choice of determining who (if anyone) is in the wrong and seek to correct it. Heroism isn't supposed to be easy, it is supposed to be wrought with peril and there are missteps.
Another thing the Paladin 2E book does is propose various degrees of ethos violations. That only conscious evil acts taken by the Paladin will result in losing one's powers without atonement. For example, the Paladin makes a pact with a tanar'ri to gain more power(s) knowing full well what that being is and the consequences. If the Paladin was tricked by the tanar'ri by disguising its nature, then the character would be permitted to undertake atonement if the Paladin was truly remorseful. In this case, if your world view is that "if my powers can be taken away because of some arbitrary rule, screw this!" well you're clearly not remorseful and acting chaotically, and thus would either have to undertake an even greater penance or simply be refused. The path of atonement, much like redemption, isn't an easy one!
Minor ethos violations could then result in varying degrees of loss of powers be it temporary or not until atonement was achieved. For example, if you chose to keep your remove disease weekly ability just in case a companion or other PC were to contract a disease in your upcoming adventure into the den of evil instead of helping a leper, you might find that you wouldn't be able to cure the disease to your friend until after you healed the leper. Or that you yourself would temporarily lose your immunity to disease.
Now, the question inevitably falls to "what is the ethical paladin code". Up to 4E, the Great Wheel or planar cosmology basically defined what were the ideals of alignment. The forces of the multiverse were such that you had an example of what it was to be a paragon in a Lawful good sense (Celestia). What chaotic evil is (the abyss), and the rest of the alignments. There was no "God of Lawful Goodness" but rather the deities that resided on those planes represented various aspects of what it meant to be of that alignment. Again, going by the Forgotten Realms, the Triad of Tyr (god of Justice), Torm (god of Valor) and Ilmater (god of martyrdom, resisting and alleviating suffering) were not the be all end all of Lawful Good but following their ideals were steps towards joining and becoming one with the plane of Celestia and ascending in a spiritual sense. As a side note, I felt the 4E change of the cosmology of D&D was incredibly foolish as it invalidated years of past material for the sake of "making it simple". But I digress...
The Book of Exalted Deeds and Vile Darkness (and lesser extent Champions of Valor and Ruin for Forgotten Realms) does go on to define what are truly evil acts based on the alignment system. Torture, regardless of the circumstances was evil. Even if it was in a "means justify the ends" perspective. Why? Because it was a concession of Good to Evil that shifted the planar balance. A lawful good fighter might not have been forced to shift alignment. Neither would the Paladin necessarily, but the latter would lose their status as one though. The reasoning being that yes, the non-Paladins could certainly say they were willing to sacrifice their morals and ideals for "the greater good", the Paladin was predicated on the ideal of Lawful good. I.e. a benevolent and just society that treated citizens and life with dignity and respect. Why does the Paladin come off as "stuffy"? Because normally he wouldn't compromise with regard to Law vs Chaos, Good vs Evil.
The other point that was brought up was the LG Paladin that lived in a society that had a Lawful evil government/culture. Then again, the Paladin could then choose not to be bound by that government in a hierarchical sense. Instead, he would work with or within the government to curb their behaviour towards lawful good. In a modern society, a Paladin would support universal healthcare but not support warrantless wire-tapping, or drone strikes without due process. The Paladin would work within legal channels to try to stop the latter two. Meanwhile, the chaotic good character ranger in the group would say "screw Obama!" and decide to form a libertarian paradise and hold himself or herself to a morally good behaviour. The Neutral good character would take the middle path, recognizing that said libertarian paradise makes it too easy for those of selfish behaviour to take advantage of the system or lack thereof, but also look towards grass roots solutions to bring about the greater good. The neutral good character puts good above considerations of law or chaos. Conversely, a lawful neutral character would go along with it so long as there was a legal basis behind the authority. The lawful evil character would try to work within the system to get the most benefit out of it. I won't go over how all the other alignments would act but that's the gist of it.
There was a very good reason why the 3E PB stated that each of the good (and also neutral) alignments were the "best" because of certain virtues. D&D being ultimately a game about heroic adventures and not a bunch of sociopaths or psychopaths looking for ultimate power to advance their own interests. This allows players to pick what virtues were most important to them and/or their characters. Yes, this is subjective to the DM and the players' interpretation at the table. But that's the beauty of the system, each table is different. In conclusion, the aim for D&D Next is stated as trying to appeal to everyone from 1E to 4E and reach out to new customers by appealing to the heroic sense of adventure and imagination. Alignments do fit into that. If they choose to make it "optional" that works too. But I'd say that alignments and what few mechanics lay behind them are probably the easiest thing to remove from the core game.