The Big Bang Theory managed a twelve-season run, and over that time, most of the main characters changed so much that they became almost unrecognizable. While some didn't have a huge arc, others changed careers, got married, had kids, even went to space... and of course, for Sheldon and Amy, won a Nobel Prize.
There are lots of ways to look at the changes that the characters underwent in the series, but one that can be surprisingly revealing is to look at the first and last line they spoke. While some end up being unimportant, the majority actually go a long way to revealing how they were first introduced, what changed, and what echoes of their early selves can be found in the later moments.
Beverly Hofstader
Yes, I can read the sign, I'm just pondering the implications. - You, forgiving me. It means a lot. Thank you.
Leonard's relationship with his mother was never easy. In earlier seasons, fans find out that as a child, she was painfully cold and distant (so much so that he created a 'hugging machine' for himself). She treated her children like experiments, and despite Leonard's incredible intelligence and success, he thought she saw him as an underachiever. However, by the end, a lot more of her humanity, her own foibles, and her motivations have been revealed, making her significantly more sympathetic. Her first and last lines show this, as she starts out painfully clinical in her first interaction with Penny, and ends up quite emotional, thanking Leonard for his forgiveness.
Leslie Winkle
Hi Leonard. Goggles, Leonard. - Happy Birthday Dumbass
Leslie's first line is a bit of a non-starter, as she is just greeting Leonard. The rest of their interaction is significantly better, as Leonard is struggling to ask Leslie out, and she's trying to heat up a cup'o'noodles with a high-powered laser, but her technical first line is a bit of a dull one. Of course, their relationship isn't really developed on the show, either, as Leslie exists largely to create a little drama. Her last line is actually part of a larger, and more telling speech at Sheldon's birthday - one that starts by saying she would usually say 'Happy Birthday, dumbass', but she has grown and changed. Of course, as usual, Leslie is played for laughs, as Sheldon thanks her and asks her to say it anyway.
Stuart Bloom
Oh, hey Leonard. Can I help you find something? - Speaking of which, where do you keep the spaghetti strainer?
For potentially the most uncertain of the characters, it's noteworthy that both his first and last lines are questions. While Stuart goes through some major changes on the show, he really never develops any confidence in himself. Beyond that, these two lines also show how important he becomes to the group over the course of the series.
Initially, he and Leonard have a friendly relationship, but it's still quite distant and clearly that of a customer/business owner. By the end, he is taking care of Howard and Bernadette's kids, and asking them about a spaghetti strainer to help potentially find something that was swallowed... certainly not distant any more!
Bernadette Rostenkowski
Microbiology. - She fell down the stairs? Oh Stuart!
Neither Bernadette's first or last line holds up well on its own, which is a shame for such an incredible character. Her first line is in response to a question from Howard on their first blind date, when he asks what she is studying (and then makes a bad joke, which falls flat). Her final line is also a response, this time to Stuart, who is looking after her kids and tells her that her daughter fell down the stairs and lost a tooth.
Howard Wolowitz
Wait till you see this! - I wasn't sure what to do, now I am. We're going home.
Howard's first line comes when he is walking into the apartment with Raj, and the two of them are excited about telling Leonard something. His final line comes when he and Bernadette are with the gang to watch Sheldon and Amy get their Nobel Prize, and they are freaking out about being away from the kids. He tells Sheldon this, and Sheldon replies with his usual selfishness, leading Howard to say they are going home. (Spoilers, they don't).
While these may seem like fairly 'nothing' lines, they actually say a lot about how Howard has grown. Initially, he is always with Raj, and the two basically have a joint first line. By the end, though, his priority is Bernadette and his family. In addition, in the early seasons, Howard was cowed by Sheldon... but finally, by the end, he can stand up to him.
Raj Koothrappali
It's fantastic! Unbelievable! - I know.
Raj, sadly, is the only one of the main group who doesn't achieve his goals. Everyone else gets married, but despite his desperation to find love, Raj ends up alone (albeit sitting next to Sarah Michelle Gellar). Howard goes to space, Bernadette and Penny launch careers, Amy and Sheldon win a Nobel Prize, but Raj... basically stays the same.
Which may be why his lines are so... boring. His first line is a follow up to Howard's, and really just echoes the best friend he was constantly with for the first several seasons. His final line is a throwaway joke with Sarah Michelle Gellar, which is sad to see. The line itself may be funny, but Raj deserved more.
Amy Farrah Fowler
Excuse me, I'm Amy Farrah Fowler, you're Sheldon Cooper. - And now, speaking of not listening, my husband, Dr. Sheldon Cooper
Amy Farrah Fowler's introduction to the series was amazing, as she and Sheldon end up on a blind date thanks to a website that Howard and Raj set up Sheldon's profile on. Their initial date sees Amy acting almost exactly the same as Sheldon, showing what a perfect pair they really are. And although Amy grows, and slowly reveals that she is much more complex and less of a Sheldon-clone than we saw at first, she is still a perfect match for him... as shown by her final line, referring to Sheldon as her husband. Of course, the lines that come before this are actually significantly more meaningful, as Amy gives her Nobel Prize acceptance speech, encouraging young women to get into the sciences.
Leonard Hofstadter
Agreed. What's your point? - How long is it going to take you to get ready?
Leonard's anxiety and uncertainty is one of his defining traits, so perhaps it is no surprise that his first and last lines (like Stuart's) are both questions. His first is to Sheldon, as Sheldon tells him about the famous 'Double Slit' experiment, and he asks what Sheldon's point is (turns out, he doesn't have one, but thinks it would be a cool t-shirt). In the end, he is asking a pregnant Penny struggling with morning sickness about how long she will take. The biggest takeaway here, though, is that Leonard's focus has shifted - from Sheldon to Penny.
Penny
Oh, hi! That's nice. - Thanks Sheldon, I haven't told my parents yet, but thanks.
Penny's first lines are when she initially meets Sheldon and Leonard... and there are a few more 'hi!'s in there, too. She seems distant but pleasant, and the gag here is really all about Sheldon and Leonard. In the end, though, she gets a sweet callout in Sheldon's speech, and thanks him for his kind words.
One of the more interesting things about this is actually that Sheldon's speech to Leonard and Penny includes a callback to that same scene, just a little later. Sheldon reminds them that Leonard, who falls for Penny immediately, says that their 'children will be smart and beautiful'... and now that Penny is pregnant, he is sure that will be true.
Sheldon Cooper
If a photon is directed through a plane with two slits in it, and either slit is observed, it will not go through both slits. - I apologize if I haven't been the friend you deserve, but I want you to know, in my way I love you all. And I love you. Thank you.
Unsurprisingly, Sheldon's first and last lines are big ones. His first line is the start of an explanation of the 'Double Slit Experiment' - an experiment that is well known to anyone with an interest in physics, but does double-duty of sounding wildly complex and scientific to anyone else. It sets the tone for the show, and the character, nicely. His final line, though, is at the end of a final speech which is long and heartfelt, individually thanking all his friends for all that they have done for him. It's a perfect way to show how much he's grown.