Hagrid is one of the most beloved characters in Harry Potter - and one of the least complicated. In a magical world where many of the heroes are deeply flawed, Hagrid is simply charming, and his good intentions and kindness to all living things mean that even his flaws (like his tendency to spill secrets!) are easy to overlook.
However, despite how beloved he is, sometimes Hagrid gives some flat-out terrible advice, especially to Harry. There are times when he definitely does know what he is talking about, but just because Hagrid is good with magical creatures, it doesn't mean that he is equally good with human situations.
Best: All The Times He Accidentally Helped Harry
This may not have been intentional advice, but Hagrid actually gives Harry, Ron, and Hermione a whole lot of great tips on their various adventures. From telling them how to get past Fluffy in The Philosopher's Stone to helping them break the rules in later movies, Hagrid can always be counted on to 'accidentally' help them figure out what to do next.
Worst: Telling Harry To Cheat
Admittedly, it seems that everyone else was cheating too, and Hagrid passed this one off by saying that cheating is a long-standing tradition of the Triwizard Tournament, but still. Hagrid has a surprising indifference to the rules (and always has), and encourages Harry to ignore them, too. He actively tells Harry to cheat in The Goblet of Fire, and even helps him, by taking him to see the dragons that he would have to face in the first task.
Best: Don't You Think On It Hermione, Don't You Think On It For One Minute
When Draco first calls Hermione a 'mudblood', the slur has to be explained to Harry, who doesn't understand why it is such an insult. However, it is Hagrid that gives the best advice in this situation, telling Hermione to hold her head up high and not let Draco's awful language get to her.
He reminds her of her talent, of how many talented muggle-born witches and wizards there are, and that most people in the magical community have some level of muggle blood in them, too.
Worst: Threaten Your Cousin With Magic
Admittedly, Dudley is a terrible cousin to Harry, and spends plenty of time bullying him, but still. Hagrid not only actually uses magic to transfigure Dudley when they first meet (giving him a pig's tail), but he actively encourages Harry to threaten his cousin with 'a nice pair of ears to go with that tail of his'. He doesn't suggest Harry actually do this, because it would be illegal given his age, but he does remind him that Dudley doesn't know about underage magic. Encouraging magical threats is hardly positive advice.
Best: There's A Storm Coming Harry, We'd All Best Be Ready When She Does
While Hagrid might not always seem like the brightest guy at Hogwarts, this quote shows that he is actually pretty perceptive, on this big stuff. He isn't just advising Harry to be ready in a more literal sense (although he is doing that too), but advising Harry to look ahead, to read the signs from history and apply them to the present, and not to get too comfortable with the idea that bad things can't happen a second time.
Worst: Don't Tell Anyone About...
Despite the fact that fans love Harry, Ron, and Hermione's friendship with Hagrid, there are times when it definitely verges on inappropriate - like when he tells them to keep his secrets. The biggest one is, of course, Norbert - his illegally obtained baby dragon.
However, especially in the books, there are times when Hagrid asks children to keep his secrets, advising them to lie to their Professors and break the rules.
Best: Be Kind To All Living Things
Hagrid's best trait is, by far, his love of all living creatures. He refuses to see magical creatures as frightening, bad, or monsters, even if others would be terrified of them. Instead, he stubbornly sees the best in every creature, and tells Harry & Co to do the same. He gives them incredible advice on dealing with specific creatures (like Buckbeak and the Thestrals) that help them out, but his overall attitude of looking for what makes something special, not scary, is an incredible one to pass on.
Worst: Follow The Spiders
On the flip side of Hagrid's love of all things monster-y, possibly the worst advice he ever gave Harry and Ron was to 'follow the spiders' in The Chamber Of Secrets. This, of course, led them into the Forbidden Forest, and to Aragog, who was more than happy to have them eaten! Thankfully, a magical car just so happened to be driving around to save them, but there's no doubt that Hagrid's good faith nearly got his young friends killed.
Best: What's Comin' Will Come, And We'll Meet It When It Does
This is definitely one of those times where Hagrid got it right - and was able to deliver the only appropriate advice: that when there is fear and stress about bad things coming, the only thing to do is accept that it's on the way, and stand tall to meet it. This is where Hagrid's real strength shows up, not just in his size, but in his ability to accept things as they happen, and face them with real courage.
Worst: All Slytherins Are Bad
One of the first things that Hagrid tells Harry is that 'there's not a single witch or wizard who went bad who wasn't in Slytherin'. It does a solid job of setting Slytherin up as the 'evil' house, but it's just plain not true. There are good witches and wizards in Slytherin, and more to the point, there have been 'bad' people who were not Slytherins. Peter Pettigrew and Professors Quirrel and Lockhart are obvious examples of that. But not only is this advice wrong, but it sets Harry up to hate and mistrust an entire quarter of Hogwarts students.