This might take a while since I have so many:
4 Cobra MK III: 1 is my main ship, I love her to death, setup for combat but I use it as a mission runner and roleplay. 1 purely as a smuggling ship, stripped down to save weight crap shields and all cargo. 1 for canyon running in Alliance space, setup the same as the smuggler Cobra cause every thinks it can't turn well enough to canyon run that's why I got it to prove them wrong. The last 1 I got cause I was 280 LYs away from my main Cobra so I bought it to save time. Has no purpose atm but I can't sell a Cobra. No other ship matters really.
Sidewinder: My first ship, she helped me get to the point to buy the Cobra so naturally I love her for it. That and she is still one of my top 5 ships in elite.
Adder: Bought at first to me a miner, is now my explorer. I have a long term goal to get that ship to the galactic rim. I know the Asp is a better ship for that but I want to try with the Adder. It's that ship or I'm not leaving the bubble.
2 Imperial Eagles: 1 for basking, the other for basking in Alliance space
Hauler: Taxi, also roleplay reasons.
Imperial Courier: My PVP ship. Railguns all day baby
Imperial Clipper: Used to be my main combat ship. Has no purpose atm other than basking.
Python: My second favorite ship, second only to my beloved Cobra MK III. She's my main combat ship now. It's just a bigger Cobra.
Orca: I fell in love with it cause it's so fast, makes whale sounds and I can use it as a smuggler. The one thing it's can't do well is fight, unless you count ramming as fighting but I ram things in every ship I own.
Viper MK IV: Mini Python. Use it as a cheap Combat ship that I can afford to get blown up. Granted that's only happened twice, once from friendly fire
Type 6: Miner, I recently went blind in 1 eye due to a car crash so sometimes I need to chill to regain my focus. Easiest way to do that and still be playing is mining so T6.
Keelback: Ummm.... 2.2 might save this ship but right now it's just a flying coffin. I'm good in a fight, damn good, but I can't survive in that thing if my life depended on it. Chances are high I won't be keeping it once I hit my goal of owning a Cutter.