Maverick: I feel the need...
Goose: ...the need for speed!
Maverick and Goose say this to one another before they go flying together. It is clearly a little inside joke call-and-response that they like to engage in before they go flying. The exchange shows their camaraderie and closeness, and highlights the way that Goose is ready to pick up whatever Maverick puts down. They are a simpatico duo, that's for sure.
"That was some of the best flying I've seen to date — right up to the part where you got killed."
After Maverick takes a bunch of risks in a training session, Jester, one of the instructors at Top Gun, scolds him for his carelessness and his stupidity in the air. This line highlights the fact that Maverick still has a lot to learn, and while he may be a highly-skilled and confident aviator, he also has some blind spots, and in the Navy, those blind spots could cost him his life. Jester illustrates to Maverick that he has to be smart in addition to being good.
"Maverick, it's not your flying, it's your attitude. The enemy's dangerous, but right now you're worse. Dangerous and foolish. You may not like who's flying with you, but whose side are you on?"
In the locker room, Iceman confronts Maverick about their differences, and echoes what many people in Maverick's life have said about his reckless attitude. He calls attention to the fact that Maverick is a good pilot, but he doesn't seem to care about the greater good or about his teammates. Iceman distinguishes between Maverick's abilities and his attitude, stating that Maverick's attitude is the thing that needs work.
"You don't have time to think up there. If you think, you're dead."
In class, Charlotte uses Maverick's antics with the MiG-28s in the Indian Ocean as an example of what not to do. This makes Maverick defensive and he says this line. According to him, flying and thinking do not go hand in hand, and a pilot has to be impulsive. He is defending his flying as a person who actually has to do it, and arguing with the woman he loves about his own competency as a pilot.
"Well, I am going to finish my sentence, Lieutenant. My review of your flight performance was right on...but I held something back. I see some real genius in your flying, Maverick, but I can't say that in there. I was afraid that everyone in the tax trailer would see right through me, and I just don't want anyone to know that I've fallen for you."
After Charlotte makes an example of Maverick and embarrasses him in class, he speeds away on his motorcycle, angry to have been played for a fool. Charlotte is close behind him in her convertible, and they eventually pull over and talk. She doesn't budge on her stance that her review was "right on," but adds that, personally, she is very impressed by his flying. She explains, in a heated exchange, that part of the reason she used him as an example in class was so that no one would know that she is in love with him. In this moment, Charlotte expresses not only her admiration for Maverick as an aviator, but her love for him as a man.
"Every time we go up there, it's like you're flying with a ghost."
Goose asks Maverick about why he can get so reckless in the air, and guesses that it might have something to do with the mysterious disappearance of his father, who was also a naval aviator. In this line, he informs Maverick that sometimes it can difficult to fly with him, because Maverick is so caught up in the past and in the memory of his father, a "ghost."
"God, he loved flying with you, Maverick. But he'd have flown anyway ... without you. He'd have hated it, but he would've done it."
After Goose dies, Maverick goes to his house, where he finds Carole crying in a room. The old friends embrace, and Carole, through tears, says this to Maverick. The line shows just how much Goose loved flying, but also that the reason he loved flying so much was that he got to do it with Maverick. In some ways, it is Carole's way of telling Maverick that he can let go from feeling responsible for Goose's death, and instead focus on the positive impact the two men had on each other's lives.
"Don't screw around with me Maverick. You're a hell of an instinctive pilot. Maybe too good. I'd like to bust your butt but I can't. I got another problem here. I gotta send somebody from this squadron to Miramar. I gotta do something here, I still can't believe it. I gotta give you your dream shot! I'm gonna send you up against the best. You two characters are going to Top Gun."
In the beginning of the film, after Maverick eludes the MiG-28s, Stinger calls him and Goose into his office. He chastises the two pilots for being reckless and foolhardy, and it seems like he's going to punish the men for their antics. However, he ends up offering them both spots at Top Gun, the prestigious fighter pilot school in California. This line typifies the way that Maverick's superiors resent him for being such a, well, "maverick," and in spite of their better judgment, think he is one of their better pilots.
"You can be my wingman any time."
At the end, after Maverick has saved Iceman from the MiGs and helped make the rescue mission a success, he and Iceman make amends, and hug as friends. Iceman says this to Maverick, suggesting that he now trusts him and wants to be friends and allies as naval aviators.
"That's pretty arrogant, considering the company you're in...I like that in a pilot."
In his first class at Top Gun, Maverick alludes to the fact that he will be the best pilot in school, a rather cocky pronouncement. Viper, the teacher, says this to him right afterwards. It shows that he recognizes Maverick's arrogance, but sees it as a positive quality rather than as an expressly negative one. It shows that Viper has faith in the young aviator, and thinks that his attitude will get him far.