Every time I make a new character, it's so unique and fun at the beginning, and while I go through the main quest and everything, and then once I start doing the Dark Brotherhood and Thieves Guild, I always start turning into the exact same character, and it's so frustrating. I know I can make other choices but I find myself becoming the same character every time. Don't get me wrong, I love Skyrim more than any other game, I just wish I could change this. Does anyone have a similar problem or want to give me any tips to avoid this?

As mentioned, roleplaying is probably the best advice anyone can give you. Through roleplaying, every playthrough will be different from any before or after it. When you roleplay, your character wouldn't just be graphics on a screen. Skyrim is a living breathing world, it makes sense that your character is just as alive. I'm on my third playthrough, and I've roleplayed my last two.
My first playthrough I didn't have a plan. I just went out and played the game without any thought about who "I" was. I ended up doing a fair bit of the MQ, becoming a werewolf, joining the thieves, dark brotherhood, Stormcloaks, companions and the College. That playthrough got boring because not much presented me with a challenge. Fast travel also ruined it for me so I decided not to do it from now on.
My second playthrough was better planned. The Blind Breton; blind since birth which is a handicap he has since overcome. Due to his blindness, his other sense have become more acute and he has worked hard to train them. He has become very efficient with sword and board techniques and one hell of a marksman. He came to Skyrim to enlist with the Imperial Legion as well experience the local wildlife with some hunting. He witnessed the arrest of Ulfric but managed to avoid it and was in Riverwood by the time Alduin attacked Helgen (no exploits, glitches or mods because he was at the execution, I just ignored it as a formality) When Hadvar got to Riverwood, my character was already there. From there I did the main quest just enough to have a few dragons then went on my way to Solitude. During his time with the Imperials, he developed a case of gigantasophobia (fear of giants) when he was chased by a giant from Dawnstar to Whiterun. Because he heard the call of the Greybeards he does feel something pulling towards High Hrothgar which means that almost everytime he enters Whiterun he lools at HH (which can be seen from Whiterun) After his latest quest (the stones of Barenziah) he decided to retire to his home in Solitude where he makes his living as an armourer; he hunts still, mines, smiths and sells what he makes (I don't grind so this is a slow process). He only uses weapons and armour that he makes. I do plan on picking this character up again properly and do the main quest.
My third playthrough is fairly new, so it's not as detailed, but he has got a back story, as well as his time in Skyrim planned. I would go into it, but it's early hours of the morning. You must be getting tired of hearing something along the lines of "I would tell you but I'm too tired." lol.
I hope that helps.