D&D is seeing a surge in popularity after franchises like this have helped make it cool.
The show isn’t too far from seeming like it’s own campaign- there may be less magic than a typical D&D setting would have, but that doesn’t stop many of the characters from falling firmly into the personality of a D&D class.
Jon Snow - Paladin
Fittingly enough for the once-bastard who wanted nothing more than to be a ranger of the Night’s Watch, he still doesn’t get the role. Jon Snow would definitely be a Paladin if he were in a game of D&D.
He’s seemingly indestructible with high hit points, and his main focus is protecting as many of the people around him as he can while struggling to be the most moral person he can be.
Daenarys Targaryen - Druid
Dany may not have magic itself as it’s understood in her world, but she does have three dragon familiars. She thinks of them as her children, which fits right in with the love a druid has for animals.
Like a true druid, she’s very focused on standing up for what she believes in- even when that might not be the same beliefs everyone around her has- and she’ll stop at nothing to see those beliefs through.
Cersei Lannister - Ranger
Cersei may not fight in actual combat, but she’s definitely a ranger. Everything she does is a tactical decision- whether it’s manipulating her twin or her son, the king.
She’s also something of a loner. She only seems to have a deep connection with Jaime and her children; nearly everyone else she comes into with is only on the basis of what she needs them for at the moment. She’s always on the outskirts, doing her own thing.
Jaime Lannister - Fighter
Jaime is a bog standard fighter. He doesn’t have particularly strong faith, he isn’t a loner, he isn’t particularly noble or moral- no matter how much he may try to be at times.
What he IS good at is wading into battle and knocking heads around. Almost his whole life has been focused on nothing but fighting (and sneaking around with his sister). After losing his hand, his main concern was fighting again.
Sansa Stark - Ranger
Taking as much inspiration for how to take control over her own life as she did from Cersei, Sansa couldn’t be anything but a ranger just like the wine-guzzling queen.
She moves on the outskirts like Cersei, with few truly close people and making her tactical decisions from the outskirts as much as she can. She uses whatever she can to her advantage, taking the landscape of the political world as her cover just as a ranger would.
Arya Stark - Rogue
Arya is what most people probably have in mind whenever they think of a rogue, so it’s a natural fit for the class. Her entire style of swordplay is to compensate for her lack of pure strength and size with finesse and precision.
She also has what seems like a second sense to sniff out what’s going on and disarm it before it can come to a head. The stealth training she received in Braavos doesn’t hurt, either.
Tyrion Lannister - Bard
Tyrion is the honey tongued bard of the series, even if he isn’t actually very musical. His main strength is in talking people into seeing things his way, even if it wasn’t a way they would have ever thought of or pursued themselves.
No one can deny that he’s fairly charismatic- he manages to bring most people who want to kill him around to his side eventually. Even without an instrument, one of his main character traits are his seemingly endless stories- so he at least gets points for that.
Sandor Clegane - Fighter
The Hound changes a lot throughout the series, going from being Joffrey’s dog, to Arya’s somewhat reluctant protector, to somewhat of a monk, back to hanging around with Arya.
As he spent more time with her after leaving King’s Landing, he grew as a person and became a better one, but his tortured past would never leave him alone long enough for him to become the paladin he might otherwise have become.
Bran Stark - Druid
Bran might as well be someone’s druid character ripped off from some long forgotten game. He ends up as the only (known) remaining greenseer, essentially a nature priest of an ancient and almost forgotten group.
He can warg into basically anything he wants and control animals with it. He doesn’t have much of a personality by the end of the series other than being the creepy nature magic guy watching everyone all the time.
Ned Stark- Paladin
Ned was gone by the end of the first season, but there’s no arguing he was still one of the most important characters in the whole show. He started all of the events in motion with his adoption of Jon and keeping the secret of his true parents for years.
His stubborn adherence to honor and his refusal to bend- even when he knew the same path had killed his foster father- makes him a clear paladin, one who clearly inspired his adopted son and nephew Jon to follow in his footsteps.