Well I don't, so share away buddy!
Default ship of choice for a while
Python - 'Pink Panther'* does everything that I want, and perhaps a bit too well. That the larger ships can't dock at outposts is a 'deal breaker' for me as outposts are imho the most fun to dock at.
My favourites
T6 - I have spent more time in 'Trundle' than any other ship. Everything is A-rated, it has a fabulous cockpit view, is deceptively nimble, boosts all day, and I still use it for passenger missions. This boat is (imho) the absolute best value for money 'early' ship for everything except combat.
Cobra III - every time I get in the 'Fussy Buzzer' I turn the volume up to 11, hit boost and grin - 'nuff said.
DBX - 'Longbow' is (now) my go-to explorer. An amazing jump range, with just enough slots it's just a shame that it doesn't have the T6 cockpit. Oh well.
Honourable mentions
DBS - 'Kitty's Got Claws' is just a joy to fly, fast and nimble enough with excellent weapon placement to make combat an absolute hoot, yet vulnerable enough to make it scary too. Coming back with a blown cockpit is 'always fun'.
FAS - 'Lapsed Pacifist' is a joy to use for risky missions, or just melting NPCs at a haz-res. Sometimes I even have to look up from doing a Sodoku.
Cobra IV - 'Oh-Oh' is a great wee ship as long as I think of her as a mini Python, for only then does everything make sense.
Sidewinder - 'Ms Swan' is there when I want to travel to pick up a new ship. Stripped back to bare bones with a fuel scoop it's always brilliant to be back in a Sidey
Owned Unused
Anaconda - no matter how I try 'Geraldine' just doesn't connect, and I only use her grudgingly. There's nothing really wrong with this boat, it's good at everything and I have some nice paints and the ship-kit (I love the 'armour' near the cockpit), and in combat she's formidable with turrets... but... the thing is... I just don't connect with her and to be honest I should sell her.
Sold
Dolphin - it was fun but 'meh'.
Sold Never to Re-buy
Asp Explorer - I disliked this one so much I named her 'I Never Loved You' and promptly sold her. No where near better enough than my T6 for trading
and it looks like a cow-pat.
* why the 'Pink Panther'?