Samwell Tarly of Horn Hill was born the eldest son of Randyll Tarly. He should have been a lord but was instead was disinherited and sent to take the black and become a Brother of the Night's Watch.
While Sam's relationship with his family is tragic there are many heroes, including the Bastard of Winterfell, Jon Snow, who should be very grateful that Sam's father sent him away. The big bookish boy would go on to make quite a difference for the people around him, at least some of the time. It took Sam some time to learn, and he made more than his fair share of mistakes.
Genius - Found out Jon's Heritage
Thank the old gods and the new that Sam loves nothing more than reading. It is through reading at the Citadel in Old Town that he (and Gilly) come across the tale of Rhaegar Targaryen's annulment and, thus the truth behind Jon Snow's parentage, birth, and thus, the key to the inheritance of the Seven Kingdoms.
That's a very dangerous, but a very important secret.
Not Genius - Stealing Books
As Sam admitted to Daenerys and Ser Jorah, he fled the Citadel at Old Town with some stolen books and no official Maester's chain. The crime, as both Dany and Jorah know, is not terrible, though Sam obviously feels bad about it.
Still, when going AWOL from any organization, even the seemingly benign Maesters, it's not great to leave too many extra indications of your departure and making off with important and treasured reading material is not a great choice.
Genius - Figured Out How to Kill White Walkers
In season two Samwell Tarley becomes "Sam the Slayer" as he is the second person to kill a White Walker (after Jon Snow). He doesn't have fire the way Jon did though, he stabs one with a dragon glass blade he found at the Fist of the First Men.
It's very lucky that Sam had the blade, but it's smart of him to make the connection and even smarter that he shared the information, which will save a lot of people come season seven and eight.
Not Genius - Joining the Night's Watch
Sam always knew he was no real soldier and yet, he goes and joins the Night's Watch anyway. Yes, his father orders him to and disinherits him, but Randyll does not exactly escort his eldest son all the way to Castle Black.
If Sam was so smart why couldn't he think of somewhere else to go? Another family to turn to. Why does he not simply hike to Old Town instead of the wall to become a Maester? It's a mystery.
Genius - Found Dragonglass
While Sam's discovery that dragonglass can kill White Walkers is crucial to the Game of Thrones story, what may be even more important is the fact that he also figures out where they can all get some for their armies and allies to use.
Again, it is Sam's focus on books that leads him to the discovery of the incredible hoard of dragonglass that exists below Dragonstone. No one would have survived the battle of the Long Night without that discovery.
Not Genius - Leaving Commander Mormont
Sure, Sam probably would have died as well, but we'll never know. He did end up killing a White Walker, so maybe his skills would have come in handy. It's not a great idea to leave your comrades behind, especially for a girl.
The same way it was not wise of Sam to join the Night's Watch in the first place, it was then not wise to turn your back on everyone with more fighting skills than you.
Genius - Giving Jorah Mormont Heartsbane
By season eight Samwell Tarley knew himself better than he ever had. It was both sentimental and wise for him to offer his family's valyrian steel blade, Heartbane, to Ser Jorah to use against the army of White Walkers.
He understood the power of dragonglass and valyrian steel against the coming threat, and he also understood his own limitations as a warrior. Sam both wisely took Heartsbane from his family home and wisely offered it to someone who could do more good with it.
Not Genius - Letting Bran Through the Wall
It's very impressive that once again, due to his reading he knows how to open the secret entrance at the Nightfort. But, was it really so smart to let the younger brother of your best friend (who your friend thinks is dead) go out into the frozen wilderness that you just escaped from?
It's kind, and the Three-Eyed Raven certainly appreciates it, but in terms of common sense it's hard to appreciate Sam's choice.
Genius - Saving Ser Jorah
Again the world (and Ser Jorah and Daenerys especially) can thank Sam for his obsession (and trust) in books. No other Maesters would even try to get near Ser Jorah and his advanced greyscale. It was both brave and smart for Sam to look up a cure and then try it, successfully.
Without Sam's work who knows how the fight against the White Walkers would have gone in the end. It's also an incredibly kind and selfless act from Sam, which is its own type of brilliance.
Not Genius - Telling Jon About his Heritage
It was impressive that Sam was able to find out about Jon's parentage and the real story behind Rhaegar and Lyanna Stark. What was less wise was his revealing it to Jon himself. What was his reasoning while all of Winterfell waited for the attack by the Night King?
He was obviously feeling hurt and angry toward Daenerys and the revelation that she had killed his father and brother, but it's never smart to act our of spite, and that really seems like what Sam was doing here. Even if he thought Jon deserved to know who his parents were, and he certainly did, it was not a great choice to tell Jon when he did, despite Bran's insistence.