Two and a Half Men may have been off the air for more than 5 years now, but the series has left a lasting impression on the loyal-fans who continually rewatch episode-after-episode to this day.
Despite a severe speed-bump taking place in the middle of season 8 (resulting in Charlie Harper being killed off and replaced prior to the start of season 9) the series trudged on for another four seasons and kept the world laughing for as long as they could. But with that said, some characters were obviously more favorable than others, and whoever your favorite character was will assuredly give a little bit of insight into who you are.
Berta
Berta might not have been an official part of the Harper Family, but she may as well have been one since she was just as brass and insulting as the rest of them (minus Alan). Spending her time cleaning the beach house (kind of) filled most of Berta's time, at least when she wasn't getting high underneath the deck.
If Berta is your favorite character, it's possible that you've had to work for people who seemingly do leaps-and-bounds less than you do, but you're also probably a person who doesn't mind since you're smart enough to reap the benefits from those people as well.
Lyndsey Mackelroy
Lyndsey may not seem like she was a true "main" character, but believe it or not, she was around for almost half the series. As Alan's main love interest for the back-end of the show, the writers couldn't decide what direction they wanted to go with Lyndsey, eventually pushing it to the point where audiences couldn't keep track of whether she and Alan were together or not.
That said, if Lyndsey is your favorite character, you might be a tad spontaneous in nature, never really sure what direction life will take you, and constantly picking/choosing a different direction to explore and taking your time doing it.
Judith Harper
Judith might assuredly be a secondary character, but due to her being Jake's mother and Alan's ex she routinely had to show up at the Malibu beach house in order to drop-off/pick-up her son. However, Judith was never really given a chance to show any positive traits/mannerisms due to the fact that anytime audiences saw her, she was usually having it out with Alan over bills/lawyers/etc.
So, if Judith happens to be your favorite character, it's quite possible that you're a person who has also experienced a brutal divorce and understands the difficulties that it puts you through, especially when you might have a child with someone who makes it all the more complicated. But, make no mistake, you're also a passionate and caring individual... just probably not toward your ex.
Jenny Harper
Jenny was absolutely a main character, she just wasn't around for very long. After Jake departed following season 10, the "half" part of the title was missing - enter Jenny. She shows up at the premiere of season 11, announces that she's Charlie's daughter, and is then revealed to be almost as much of a womanizer as her deceased-father.
If Jenny is your favorite character, it's probable that you're a person who likes to show up at the last minute and stake your claim as king (or queen) of the castle. But be careful, for it's also a possibility that you have a tendency to not care as much about relationships as the people you get into them with.
Rose
Let's face it - Rose was a little nuts. Introduced in the very first episode as Charlie's stalker, Rose became infatuated with Charlie after spending one night together, thus beginning a series-long staple that eventually ended with Rose being the one to kill-off her beloved by pushing him in front of a train platform. Not only that, when Walden took over for the deceased Harper, Rose made a comeback and tried to ruin his life as well.
In conclusion, this is a sitcom and all sitcoms should be taken with a grain of salt - that said, if Rose was your favorite character then hopefully it was just for comedic purposes because otherwise there may be some things about your love-life that you'll want to reevaluate.
Evelyn Harper
Despite her character showing up less-and-less as the series drew to a close, Evelyn spent her fair share of time in the Malibu beach house over the years as she made life for her sons and grandson as miserable as she could. The main characteristic Evelyn displayed was the impressive ability to immaculate her family members without so much as lifting a finger.
If Evelyn is your favorite character, it's possible that you're also a person who had to endure a tedious-parental figure who nagged about your every flaw, thus making you the perfect audience member to laugh along at the situations that are all too familiar to you.
Walden Schmidt
As stated, Walden was brought in to replace Charlie after he met his demise at the conclusion of season 8, and the character played by Ashton Kutcher quickly became comfortable in his new Malibu beach house. After a failed suicide attempt from his marriage ending, Walden buys the beach house and allows Alan to continue living there (rent free) and spends four years trying to find the next love of his life.
With that in mind, if Walden is your favorite character, it's very likely that you're a head-in-the-clouds romantic who is always looking for "Mrs. Right". Also, you might have potentially started your own company and sold it to Microsoft for a billion dollars... but that's less likely.
Jake Harper
Jake's a hard character to pin-point - on the one hand, he's the only child on the show and offers the only sense of innocence in the entire series. On the other hand, as the series grew and evolved over the years, Jake grew into a pot-soaked degenerate who very much emulated his late uncle.
So, if Jake is your favorite character, maybe you're a person who prefers wholesome-humor over vulgar-humor... but on the other hand, maybe you're a person who also grew into a bit of a party-goer and enjoyed watching Jake evolve and grow in the same way you did. Or maybe you just like fart jokes.
Charlie Harper
Charlie was a character who started his reign as the king of the world... which quickly led to a meteoric fall as the tiger's blood in his veins ultimately killed him. In the beginning, Charlie was a slack-off jingle writer who spent his days sleeping with any woman he could find, but by the end of the series, he had become a sleazy, drug-riddled sycophant that was killed off and replaced.
Not much can be said if your favorite character is Charlie Harper, other than the fact that you don't mind that Charlie Sheen almost derailed the entire series with his actions. That said, perhaps you're a person who can look past the actor's imperfections and you simply enjoy Charlie because you enjoy laughing at sitcoms.
Alan Harper
The only titular character to make it from start-to-finish, Alan was always known as a bit of a leech when it came to taking money from the people around him, but that was more so due to bad financial luck throughout his life, not in a miserly way. Even so, he made a point of trying to be a good a friend/person as much as possible in order to compensate for his lack of monetary value.
So, if Alan is the character you enjoy watching the most, it's possible that you're a person who has also found themselves in tough financial situations who has been lucky enough to have people around to help pick you up when you're down. But make no mistake, no matter how much you seemingly take from your friends and family, you always do your best to pay it back (or at least forward).