Supplement I for original D&D, not the campaign setting (I find it hard to use pre-published settings). A lot of things I love come from there, as well as a lot of things I don't like one bit.
I have a love-hate relationship with variable weapon damage. Yes, it provides a reason to use different shapes of dice. Yes, it gives fighters a clear advantage in that only they can use the most damaging weapons (in B/X, those are the pole arm and the two-handed sword). But using different dice for different weapons - or even for the same weapon, used against different opponents - slows down the game, and is confusing for brand-new players. Particularly the variety whose idea of an RPG is Final Fantasy XIII. Except for the encounter tables, OD&D can really be played with just several d6's and two (old-school, 0-9 twice) d20's. This is just another instance where the commercial circumstances, i.e., not wanting to sort out the extra polyhedrals from the boxed sets, led to something that sticks with us to this day.
Exceptional Strength is one of those things that I love in principle, but in practice is a little weird. Whereas the curve for Strength modifiers for "to hit" and damage rolls in B/X (and, by extension, BECMI) is a straight -3 to +3, the versions of the game that use percentile Strength rolls (OD&D and both iterations of AD&D) have two different curves, neither of which amount to +3 without the character being a spectacularly ripped fighter, ranger, or paladin. Plus, TSR's official AD&D2 character sheet uses tiny boxes for the ability scores, so one would have to use the old calendar technique of diagonally splitting the Strength box to write a percentile score.
The thief class is necessary in OD&D for anyone who isn't an obsessive fan of Myst or Portal. It's also necessary for anyone who, like Delta, decides that the cleric class may not be a good fit depending on its implementation. At least three basic types of characters are needed so that a player doesn't feel hemmed in; even Tunnels & Trolls used three basic classes. (Granted, one of them was really a hybrid of the other two, but it's still nice to have a little bit of choice.) In the amorality of D&D's early years, I imagine that most referees would have allowed the thief to steal from their own party members... if they could get away with it, and live.
Paladins are, well, a mixed bag. I think they're necessary to provide a warrior class that is neither directly going to conflict with other players (the barbarian from Unearthed Arcana comes to mind...) nor extremely limited in their actual special abilities (like the original ranger). Their role in the setting needs to be determined, though; considering the unlikelihood of rolling a 17 Charisma on 3d6 in order, the referee should have plenty of time to think about that.