What is the most powerful/versatile character?

[Vincent Dragon]

How much stuff is possible to put into one character with 20 levels?

-20 all stats
-All cantrips (maybe even all spells)
-Proficiency on everything (saves, skills, etc)
-What else is there?

So how much of these (and more things i don't remember) are you guys able to optimize in this guy?

[Thisguy_]

In before Wizard is selected as his class.

[Malifice]

I quite like Half elf Lore Bard 14/ Paladin 6 with the criminal background.

Proficiency in 10 skills, 3 instruments, thieves tools. Expertise in 4 skills. Half prof in the rest.

9th level spell slots. All armor and all weapons. Melee juggernaut with extra attack, fighting style, smite, haste, mirror image and elemental weapon. Buffing and healing taken care of with lay on hands, song of rest, bardic inspiration, spells, aura. Charisma to all saves for defense.

[Arcuriel]

I ran the numbers a while back, and I don't think it's actually possible to obtain 20 in all 6 stats, at least before magic items.

[lordshadowisle]

I ran the numbers a while back, and I don't think it's actually possible to obtain 20 in all 6 stats, at least before magic items.

Not with point buy, but it's theoretically possible with stat rolling. With 18's for every roll at stat creation, any race can max 20's in all stats with 5 ASIs, and much less if human.

Of course, by rolling we should never be seeing such stat arrays, but then again...

[PoeticDwarf]

How much stuff is possible to put into one character with 20 levels?

-20 all stats
-All cantrips (maybe even all spells)
-Proficiency on everything (saves, skills, etc)
-What else is there?

So how much of these (and more things i don't remember) are you guys able to optimize in this guy?

If you want skills, you can get start as rogue, one level bard and one level ranger for 6 skills, halfelf for 8, background for 10, multiclass knowledge cleric for 12.
If you have 3 levels in bard, you have 3 skills more for a total of 15.
So a 3 bard 1 cleric 1 rogue 1 ranger and 14 monk has 15 skills with skilled you have 18, so all skills.
Because you're a halfelf you can with pointbuy get in stats: 14,14,14,13,12,12. 5 improvements make 14,14,14,15,14,18
A human fighter can get the highest scores.

14,14,14,13,13,13 7 improvements make 18,18,18,14,14,13 but that's without magic items and 4d6b3.

[GiantOctopodes]

My personal pick for skills would be a Half Elf Assassin Rogue 12 / Lore Bard 4 / Knowledge Cleric 3 / Ranger 1 with the Charlatan Background, with one of their ASIs going to the "Skilled" feat.

They have a total of 18 skills (4 from Rogue, 2 from Background, 2 from Half Elf, 2 from Knowledge Cleric, 4 from Bard, 1 from Ranger, and 3 from the "skilled" feat), enough to provide proficiency with *all* skills (there are 18 total available).

They also have proficiency with the Thieves Tools, Poisoner's Kit, Disguise Kit, Forger's Kit, a Musical Instrument, and one additional Tool proficiency of their choice. Any tools with which they are *not* proficient, they can become proficient with using their Channel Divinity Feature.

Of those proficiencies, 8 of them (4 from Rogue, 2 from Bard, 2 from Knowledge Cleric) are doubled.

Any ability check with which they are proficient (again, potentially all of them) they cannot have a result of less than 10 for their die roll, and any that they somehow are not proficient with, gain half their proficiency bonus.

You can have Expertise on 2 more skills if you switch it to Lore Bard 10 / Rogue 6, and otherwise leave everything else the same, and you gain superior spellcasting by doing so, but you lose out on Reliable Talent, which is (for this character) not an even trade whatsoever, in my book. There is definitely something about having a 0% chance of getting a result of less than 16 + your ability score modifier (or, in the case of 8 skills, 22 + ability score modifier) that is quite appealing. The character also manages to gather up a total of 5 ASIs despite the heavy multiclassing, which should help with their extreme MAD situation (minimum 13 Dex, Wis, and Cha) to still end up with decent scores, as EnderDwarf outlined above. Note that for such a character I'd personally leave Str and Int as dump stats, and try your darndest to find the Gauntlets of Ogre Power and Headband of Intellect , allowing you to achieve 4 stats of 18 or higher.

[Citan]

I quite like Half elf Lore Bard 14/ Paladin 6 with the criminal background.

Proficiency in 10 skills, 3 instruments, thieves tools. Expertise in 4 skills. Half prof in the rest.

9th level spell slots. All armor and all weapons. Melee juggernaut with extra attack, fighting style, smite, haste, mirror image and elemental weapon. Buffing and healing taken care of with lay on hands, song of rest, bardic inspiration, spells, aura. Charisma to all saves for defense.
I heavily concur with this.
Paladin path provides you a solid melee potency with extra attack and smites, and many healing spells. Especially since Paladin knows all spells from his list.
Bard provides additional spell slots, many utility/buffs (so you have many ways to always use a bonus action for good profit) and additional versatiliy through Magic Secrets.
As well as large skill proficiency and RP utilities...
And both share the same primary stat (CHA) and can focus in DEX instead of STR if you'd prefer.
One of the best synergies ever between two classes imo.

Beyond that, there are many "versatile" builds but you'll eventually lose some raw power in late game... Can be very fun to play though.

For example, Paladin 6 / Warlock 3 / Sorcerer 11
1. Paladin all the same (melee + smite).
2. Sorcerer for offensive spells and Metamagic synergy, like...
You don't have Warcaster feat? Just cast a spell with Subtle metamagic.
Or, you have three creatures to take care of? Cast a Twinned Hold Monster (and pray ^^). On success, you have now only one guy to be worried about.
Or, you're in a pinch and would like a way to hit them again in your turn while securing your escape? Smite them then cast a Quickened Invisibility and retreat silently.
3. Warlock not strictly necessary, mainly here to get 6 MP per short rest, Hex, Armor of Agathys, Eldricht Blast AND your preferred Pact (like a special Familiar to get resist spells or a Tome for useful cantrips and rituals).
Fluff synergy also if you take Oath of the Ancients / Fey Pact, or Vengeance / GOO.
Sure, as a caster, it's far weaker than pure spellcasters. As a Paladin though you're powerful, although in a different manner than the traditional Paladin: you sacrifice some of the best Paladin spells, extra 1D8 damage per hit (partly compensated with Hex) and interesting oath features to get more spell slots and versatility, notably in some higher level spells... :) Otherwise, a more classic build would be Paladin 12/ Sorcerer 8: basically a Paladin with just more spell slots and a few offensive spells.
You can even adventure further in the multiclassing for further versatility (an ongoing example (http://www.giantitp.com/forums/showthread.php?422838-Opinions-about-a-strange-heavy-CHA-based-multiclass-build-%29)) but then come builds that are hard to get online and not min-maxed at all... Just original, funny and packed with options. :)

With all that said, a "plain" Bard is already highly versatile as it is if you want to play without planning too much ahead (just a few levels in an offensive class may be in order if you want to take a good share in direct damage).

EDIT : Sorry it seems I strayed from initial topic from OP... To get back on track...
1. For "all skills", GiantOctopodes gave you the info. Note though that you cannot have proficiency in ALL skills, since each toolset has its own skills. Having all 18 "main" skills is easy though, and the Knowledge CD covers the real needs on a case-by-case basis.

2. For all stats: only doable with Grimoires that up the stat or very rare magic items, so totally DM-dependent. Otherwise, only option is being pure Fighter (for the larger number of ASI) and using "dice rolls" instead of point-buy to get (very) lucky starting stats.

3. For all cantrips: well, before the publication of Elemental Evil, it was doable (although totally broken in MAD). Basically...
a) First take at least a level in each spellcaster class:
So Bard 1 / Cleric 1 / Druid 1 / Sorcerer 1 / Warlock 1 / Wizard 1 gives you 2 + 3 + 2 + 4 + 2 + 3 = 16 cantrips.
b) Go up to 3 in Warlock to get Pact of the Tome (3 bonus), 2 Land Druid (1 bonus), choose Nature or Light domain for cleric (1 bonus), 2 Illusion Wizard (1 bonus), take Magic Initiate feat (as Human Variant) for 2 bonus. So total of 3 + 1 + 1 +1 +2 = 7 bonus.
Now you know 16 + 7 = 23 cantrips ! o/ As a lvl 11 character. Best bet then is to go Bard 6 (1 more with lvl, 2 with Magic Secrets) and Sorcerer 4 (another cantrip). Or go Trickster Rogue + Eldricht Knight to get the worst MAD ever... XD
Now, you're a lvl 20 character which knows 27 cantrips and only a few 3rd levels spells with huge MAD! \o/ Nearly all the cantrips from PHB, far from the count if you include EE...
Note, though, that it IS actually one of my PNJ: he's a master for many magic schools, and rumored to be the one that actually CREATED those various cantrips... No one knows how old he is, some says many centuries... :)

4. For all spells: not doable, but acceptable result possible. Basically take a Wizard (since you can potentially find and copy every spell available to a Wizard), with just a few levels dip in a class to get some exclusive spells (like Warlock).

[GiantOctopodes]

Note though that you cannot have proficiency in ALL skills, since each toolset has its own skills.

I do want to point out that it is technically possible to get all skills (at least all published ones) since you can spend 250 days and 250 GP to train a tool proficiency or a language. With all 18 "actual" skills in place, if you had the time you could get all the tool proficiencies and languages done, though it would take well over 20 years of downtime and would cost well over 7,500GP to do so (specifically it would be 22 years before you finished the tools, and I'm not sure how many languages there are so I couldn't give a hard and fast timeframe on that one.

(Anyone know how many there are? Common, Elven, Dwarven, Gnomish, Halfling, Draconic, Orc, Goblin, Infernal, Celestial, Primordial, Auran, Terran, Ignan, Aquan, what else?)