I remember, when playing D&D 3.0, that the bulk of the time was spent on banter, turn-based combat resolution and moving from room to room, searching for items (and equipping them), avoiding/surviving traps and being given environmental descriptions. This would be preceded by a somewhat lengthy character-creation phase and punctuated by character progression. This all from the third edition of the first (influential/popular) P&P RPG system. There might be a bit of "role-playing" (bad acting) but that was chiefly as motivation for the other activity.
So, in P&P RPGs, one has banter, challenges (combat, traps, puzzles), exploration, power progression (through improving character statistics and adding new abilities, or through gaining equipment giving equipable/reversible stat-gain and ability-gain), usually character creation (one could just use pre-made characters) and some motivation for the whole exercise, from something as banal as "kill the evil wizard" to something more interesting.
Banter, challenge, exploration, power progression (stats and equipment), usually character creation and motivation.
While some of the earliest CRPGs were multiplayer, they came to be thought of, mainly, as a single-player genre, so banter was lost -- "banter" in games like Baldur's Gate is, to me, just a component of motivation: "these characters interest me, so I want to know more about them and their world" (i.e. "I want to explore and find more such interesting stuff").
CRPGs then have challenge, exploration, motivation and power progression (stats and equipment), all as major parts of gameplay (i.e. the player spends non-trivial time thinking about them: "how do I defeat this enemy?", "where(/which way) should I go next?"/"what should I do next?", "I should save my vault by finding a water chip"/"I have woken in a mortuary, I must find out what is going on"/"I must escape this dungeon/barrow-mound/mortuary/whatever"/"I must kill the evil X", "a new weapon -- cool! Should I use it? What should I drop?"/"Level-up! More killing ability or better defence/lockpicking?" -- notice that most of these involve making decisions, I think Sid Meier said something like "Gameplay is a series of interesting choices") and often character creation up-front (essentially a bunch of power-progression, from (almost) nothing, at the very beginning, which is arguably a bad thing as it requires either guessing or prior knowledge of the game before play -- i.e. metagaming).
There are games, like Doom and Doom 2, which are clearly inspired by P&P RPGs, having challenges (three pinkies going at you in a small dark room, say), exploration, motivation (er... destroy the demon hordes! Not a lot, but enough) and some power progression (no visible stats, but the equipment has stats and you pick up new weapons and ammo for existing weapons, though there is little long-term thought about weapons as there is the ability to carry everything), but no character creation (but many RPGs also lack that). Why are they not RPGs? Well, the motivation is a bit weak and the power progression is both simple and reversible* -- if you run out of all ammo, then your melee attack is just as weak as it was at the very beginning (if without the temporary power-up) -- plus, when the last gun is gained there is no more progression and, as stated earlier, the progression does not dominate thought much (partially because all/any decisions are reversible or transient). Doom is not really an RPG.
*note that reversibility is not a disqualification for an RPG, though it makes sense for many modifications to a human(oid) character to be irreversible. A game featuring only robots could have hardware and software upgrades (even duplicating a character and copying over all its knowledge, skills and memory!), so that essentially all stats were a function of the equipped inventory.
I have read about games criticised for not having challenge (indeed, called "not-games") -- these are clearly not RPGs. Even if RPGs can be very easy, they at least offer the illusion of difficulty and the theoretical risk of failure/reload -- and the challenge could, theoretically, be "how quickly/efficiently can I get through this?"*, as much of the gameplay of a dungeon crawler is resource optimisation, as the challenge/failure is/results-from resource exhaustion.
*most people would rather not watch a movie at double speed, so there is a bit of a difference.
To deal with some (facetious) examples:
Pong: No exploration, little motivation (probably just banter from your human opponent), no power progression (as far as I know) -- not an RPG.
Pacman: Not really any exploration (you see the whole map at once, and seeing new maps as one continues does not really count), little motivation, trivial/reversible power progression -- not an RPG.
The Sims: Challenge and motivation are what you make them (i.e. little inherent), trivial exploration, power progression... maybe, but to what end? Not an RPG.
Thief Gold: Much exploration, significant challenge, detailed motivation and world-building, but little/trivial power progression (no visible stats, no equipment carryover from mission to mission -- there can be resource exhaustion, but only within a mission; overall, not a dominant part of gameplay) -- not an RPG, but certainly hitting some of the same buttons.
Deus Ex: Much exploration, some challenge (at least at the beginning, on Realistic difficulty), detailed motivation and world-building and much power progression -- certainly an RPG. It is also an FPS, to some extent (i.e. not very good as an FPS) -- it is both, the RPG part makes it great. FPS-RPG hybrid.
Wizardry 8: Much challenge (if only the battles were faster...), significant exploration, reasonable (though cheesy) motivation and a complex power progression system that will certainly give the player much reason for thought, plus multiple character creation (i.e. a big hunk of power progression at the start). Of course, it is an RPG.
Dungeons of Daggorath: Challenging (well, I kept dying), very simple motivation (kill the evil wizard! OK given that it was 1982, though arguably sufficient even for new games), exploration required to find and kill the evil wizard (and find items to allow success) and simple power progression (inherent strength improves through a process the player does not control, but equipment does matter) -- just about an RPG.
Wizardry 1: Challenging, very simple motivation (I imagine, I did not have a manual when I gave it a short try), much exploration, significant power progression through level-up and equipment (I suspect -- I never got that far) -- it is an RPG.
Super Metroid: Challenging, much exploration, decent motivation (though the setting did not really grab me) and the power progression is trivial -- one explores to get powerups, but there are few real choices (turn this powerup off to make this bit easier, then back on and continue); it is not an RPG, though (like Thief) it hits some of the same buttons.
Castlevania: Symphony of the Night: A little challenge, much exploration, decent fun/cheesy motivation and as for power progression, well, there is more to it than in Super Metroid, with some mutually exclusive equipment giving meaningfully different abilities and an entirely non-interactive level-up system -- the player can choose to pay a lot of attention to the power progression, but can also ignore it and complete the game without much difficulty with somewhat suboptimal equipment. It has about as much RPG in it as Dungeons of Daggorath, so I suppose it is an RPG, but the power progression is weak enough compared with the action-platform gameplay that the extent of its RPG-ness depends on one's play-style. Platformer-RPG hybrid.
Fallout: Some challenge (simple turn-based tactics combat), much exploration, detailed motivation and world-building, and power progression through cool items and an interesting character system, with single character creation. Of course, it is an RPG (it would not have been a very good turn-based tactics game -- Tactics-RPG hybrid, or is that going too far?).
Planescape: Torment: A little challenge, much exploration, detailed motivation and world-building and power progression that, while not overly complex or fraught (given that combat was rather easy) was quite interesting, linked to the motivation, with entertaining item descriptions and stats that determined what and how much extra text (motivation) one would get (i.e exploration of the setting through dialogue). Certainly an RPG.
Final Fantasy 6: A little challenge, some/weak exploration (I do not recall getting any important equipment that way, and elements of the setting and story were mainly revealed in a set order, limiting the incentive for exploration to taking the most obvious route), detailed motivation (though I was not particularly intrigued) and power progression through equipment (with some meaningful choices -- mainly through treating the characters as equipment and equipping different ones in the party), a non-interactive level-up system plus the espers (though with no exclusivity, any choices could be avoided by just grinding more). I would say that it is an RPG, except that the weak exploration lessens its RPG-ness somewhat (which, I imagine, afflicts many JRPGs). Depending on my mood, I would say that Castlevania: Symphony of the Night is more of an RPG than Final Fantasy 6, but I suppose it just about counts as an RPG.
Chrono Trigger: A little challenge, a cool concept/motivation, significant exploration, power progression: equipment has little complexity of choices and the leveling-up is automatic, but there are irreversible power-ups to be discovered. I would say that it is an RPG (less than Wizardry 1 or Wizardry 8, but more than Dungeons of Daggorath).
Phantasy Star 4: Mostly like Final Fantasy 6, except without the espers and with discoverable combos, and that I like it better (it has a more interesting (to me) motivation, so it must be more of an RPG!).
I have not played Call of Duty. Are there RPGs lacking significant exploration, motivation and power progressions, or non-RPGs possessing them?
I do not know about The Sims 3, having only played the original The Sims. If there are addons or mods that provide exploration (as well as adequate motivation to explore) then maybe those addons or mods qualify, but, judging from the first game, the series is clearly not intended for that kind of gameplay -- exploration may exist in many strategy games, sports games etc., but it features as a primary part of gameplay (i.e. time spent, to a great extent) in RPGs, single-player FPSs and the Thief series.
EDIT: Oh and:
Star Control 2: Much exploration, much power progression (though reversible and, if one plays very badly, a resource that can be exhausted if one runs out of fuel), significant challenge and much motivation (I really like the setting and the dialogue). It is an RPG, despite having no "characters", only a ship. Of course it is an RPG.