Let's see, I have:
1) My Original Sidewinder - I just couldn't bring myself to sell it.
2) My gifted (original backer) Imperial Eagle - only very mildly Engineered, still used from time to time.
3) My Free Cobra MkIII - never really used as it felt like a bit of an exploit to have such a good ship early-game. By the time I'd earned the right to use it (in my eyes) I had the urge to try something else. Never Engineered.
4) Asp Explorer - I so loved this ship, never been Engineered as I stopped using it before Engineers were available.
5) Type 7 - the ship that was the turning point for money making, never really Engineered it much.
6) Python - bought to replace the Type 7 in all roles, but I didn't bond with it right away, so returned to the T7
7) Anaconda - took me an age to get this ship, love it, still in regular use for multiple roles. Made big money with this ship. Was engineered, but I stripped it out for jump range.
8) Imperial Cutter - glorified trading barge...but I don't trade much now. Last saw use in a CG months ago. Lightly engineered.
9) Corvette - Combat configured, quite heavily Engineered. Totally sucked before Engineering
10) Fer De Lance - almost forgot this one! Bought it for BH with our Wing, great fun, but replaced by the Corvette before I did much Engineering.
So, just 10 ships currently, but I've also owned:
1) Viper MkIII
2) Viper MKIV
3) Vulture
4) Type 6
All before Engineering.
Scoob.