Drake, as of now.
So far I like the Crucifier, Executioner and Catalyst.
Still have to decide on Cruisers. Maybe Exequror or Vexor.
Heronfor thieveryGilafor combat (both PvE and PvP)Praxisfor aesthetics and performing fireworks showsSunesisfor versatility, mobility and travel
Abaddon, Apocalypse, Sarathiel, Ark, Sentinel, Lachesis, Legion
I have several favorites.
The Rifter will always have a special place in my heart because when I was a newbie I tackled a Myrmidon in my little Rifter and held it just long enough for my corpmates to arrive. That moment is probably why I still play this game.
The Merlin is special to me because it was my first solo PvP hull. I flew Merlins almost exclusively for years and soloed everything from corvettes to battleships in it. It was the first ship that made me feel dangerous.
I never quite succeeded in my long-standing goal to solo a strategic cruiser with my Merlin, but I came damn close one day when I caught a Legion ratting and tackled him, but couldn’t quite break his tank. However, I held him there for 45 minutes until my corp could form a fleet to help and got top damage on the kill.
The Osprey Navy Issue is special because I used a cloaky one to menace Pandemic Horde’s staging systems for 4 years, getting about 500 kills, living in space out of a cloaky Orca and never docking up, defying all their efforts to catch me.
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The Rifter will always have a special place in my heart
Amen, one of the earliest ships i used and i used a LOT of them, and lost a LOT of them, i have a Geri sat in my hangar and even though i will never use it for anything i just see it as the best version of the Rifter
A ship so iconic it was on the box
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Jackdaw is no doubt the one I spend the most time in still. While it doesn’t have the DPS to move up in PvE it was a really good choice for me to get into early on.
Currently I actually don’t have a favorite. If anything it would be Prophecy (Navy Issue), Prophecy fleets just look cool, but its still sluggish.
I used to like Catalyst best but then I realised that was just peer pressure. My favourite ship as a new player was Coercer so I have gone back to that and invented a new style of ganking I call Coercer ganking.
Many are following this fad - stay tuned!
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Is it similar to regular ganking, but with Coercers?
Yes, but we call it blood raiding!
I still remember the first time I got Coercer from NPC. It was bigger than the Punisher, but too many highslots. I didn’t have enough guns to fit it so I sold it.
Genius! 
I talk to miners sometimes, and I’ve been getting the impression that some of them are starting to feel that getting ganked with Catalysts is getting a little old.
They are going to be so impressed. I bet you’ll get a lot of great feedback.
Overall favourite would be the Tengu. That said, EHP is not enormous and at over 500m ISK its not really the sort of ship for sitting outside Jita as you are more likely to end up being the target. ( My Legion has considerably more EHP but is annoyingly slower ).
So the true role of favourite goes to the humble and seemingly puny Navy Augoror. At a mere 90m ISK, and being quite small, it actually has DPS not far short of a T2 Catalyst…at up to 15km. It has room for two neuts…or a neut and a nosferatu, and good scan resolution. It has good speed and armor tank EHP is more than for many of my larger ships. Overall a very nifty little ship…and at an ‘expendable’ cost. It’s not often you find a ship where every aspect is good.
I think that cost/benefits/risk ratio is what really matters in EVE.
For all the killing I did, as an older player, I had many favs for their time. The most fun was a cloaked Orca for driving players nuts as I forced them outta their wh. 
Dramiel.
Fast, agile, small sig.
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Back in the day I always had a soft spot for nos-phoons.
Today its the Loki, although I guess I spend more time in a mammoth than anything else.
Taranis!
the breacher is a super-versatile ship. it can be fitted for pretty much any fighting style. with 4 mid slots, you can choose an e-war of your choice.