Adventurers Have (No) Class

Aside from the not-so-clever pun, what is the title meant to express?  Certainly there are classes in an RPG.  You have to have classes, even if you don't, such as with GURPS or other "skill" games.
Yet the old school player (and young players of old school and retroclone games) would do well to consider that regardless of the character's class, they are first and foremost adventurers.  They seek adventure.  This is why the player comes to the table every session.  The player desires to have a game full of adventure.  If the character were not an adventurer then the character would be standing guard at some castle or performing daily devotions and duties in a temple somewhere, rather than descending into dungeons or ranging across the wilderness looking for monsters to fight and treasures to claim.  Essentially what I am saying is that everyone's class is, above all else, ADVENTURER-a seeker of adventure!
Adventure, which comes to us originally from Latin, but more recently via Middle English aventure, where it meant risk or chance (compare peradventure, meaning possibly from Middle English par aventure), not the normal, every day activities, but those of risk and possibly reward.  Sometimes the reward is simply surviving the adventure, but still, it implies excitement and interest, not rote activity.  This is why we play.  We want to experience, vicariously through our characters, some adventure.  An adventurer is an entrepreneur of excitement.   An adventurer seeks out adventure for its own sake (and possibly profit).  Risk and reward, death and danger, excitement and loot!  These are the things of which adventure is made.

Trust me when I say this is a cleric.  She's got a mace and some armor and that shield, but she is by no means limited to these things.

Now class, that describes a set of common characteristics used to define a player character within the world in terms of how that character best interacts with the world to solve conflicts.  Fighters are experts in physical combat.  Clerics gain extraordinary abilities through communion with higher powers.  Wizards know a thing or two about the forces of the universe that the common man calls magic.  These are the classes and they describe a loose set of abilities that are organized along common lines.  Wizards do magic.  That's a commonality.  Wizards do not wear armor.  That is a common restriction.  This does not, however, describe what the player character really does.  The player character wizard is not some sage in a tower spending all his time studying the mysteries of the universe.  The player character wizard is a seeker of adventure that descends into underworld labyrinths to face perils.  The paladin seeks to do good, actively promoting it in the world.  He could spend his time feeding the hungry and tending to the needs of the poor, but instead he rides out across the land looking for evil to face in death defying adventure.
See where I am going with this?

Pssst, that trouble you are looking for?  It's right behind you, mate.

Adventurers look for trouble; they are geared for it.  (That too was a pun, but only for gamers)

R.E. Howard's Puritan adventurer Solomon Kane is a great example.  While always attempting to be a devout man of God, the thing he loved best was adventure, even if he didn't know it himself.
"Far back in Kane's gloomy eyes a scintillant light had begun to glimmer, like a witch's torch glinting under fathoms of cold gray ice.  His blood quickened.  Adventure!  The lure of life-risk and drama!  The thrill of breathtaking, touch-and-go drama!  Not that Kane recognized his sensations as such.  He sincerely considered that he voiced his feelings when he said:  'These things be deeds of some power of evil.  The lords of darkness have laid a curse upon the country.  A strong man is needed to combat Satan and his might.  Therefore I go, who have defied him many a time.'"- Skulls In the Stars by R.E. Howard

Armor, sword, must be a fighter.  Yet he's so much more, for he is an adventurer and what you don't see is where the good stuff comes in.  He's not limited to hitting you with that sword.  He can kick you in the junk and follow it with a Glasgow kiss.

The thing to remember when playing is that the class is not a set of limitations.  The player is not required to simply fulfill a role as MMOs and modern RPGs set it.  The abilities of the class are what set the PC apart from the normal non-adventuring inhabitants of the world, like butchers and guards.  It's a mindset as much as anything else.  Eschewing the safe life of the workaday world for a life spent in peril trading risk for reward requires the character to think differently.  So you have a fighter.  He cannot cast magic spells or use most magic items.  Is this a handicap?  Nay, consider all the butchers and guards and tanners and coopers and such that cannot use magic either.  The lack of a special ability does not define the character.  You cannot lob a fireball.  Granted.  What is stopping you from lobbing a clay bottle full of oil with a lit rag in the top?  Only your imagination.  That's all.
                                Chadwick Goes Equipment Shopping:

"So this rope, what does it do?"
"It doesn't 'do' anything.  It's a rope."
"Yeah, but what are its functions when I put it on my hotbar?  Does it provide a plus to climbing?  Can I use it to make a lasso?"
"Oh (heh heh heh) you wanted a magic rope, I didn't know.  Let me just show you my 'premium' stock, oh discerning gentleman."

I recently had the joy of witnessing a youngster (well, under the age of 20), new to tabletop old school D&D, playing a dwarf (so a fighter, really) who thought to toss a rock down a hallway before proceeding, specifically to check for traps.  In that same adventure an elf (played by my wife) used a captured gnoll as a meat shield against a giant four-armed skeleton armed with swords.  This is how an adventurer thinks and acts.  An adventurer is part Indiana Jones, part MacGyver.  You look around, you ask questions of the DM, you use the environment to your advantage and you absolutely DO NOT let your character sheet dictate your actions as a set of limitations like the UI of an MMO.  An adventurer doesn't say, "I don't have a detect traps ability, so I guess I am screwed."  An adventurer tosses a goblin into a room tied to a rope so it can be pulled back if it survives!  Sure Indy is an archaeologist, but that hardly defines his character.  That is just the hook to get the adventure started.  By that same token MacGyver performs missions for the Phoenix Foundation, but again these are just ways to get the adventure started.  You are a first level Magic User.  You have 1 spell today and 2 scrolls that have no practical applications.  Are you limited by that?
Hell no.  Remember what Indy said to Sallah when asked how he was going to catch the truck holding the Ark: "I don't know.  I'm making this up as I go."
That is how to be an adventurer.  
                                Don't be like Chadwick:

"You'll be wanting the Panzer-Suit I presume?"
"I was thinking more off-tank, DPS really.  Something that buffs my hit probability and damage output, but offers decent protection."
"Son, this is a medieval city, just what the Hell are you talking about?"
"I hit things and they fall down."
"Oh, you're a FIGHTER.  Yeah, let's just get you suited up in our Warlord Starter Special, only 600,000 coppers, special today."