You are not your ship

One thing I've noticed is that many new players come to eve with the perception that their entire game life is going to revolve around one ship, one ship which will be tweaked and honed until it's perfect, everything they have is embodied in that one vessel and therefore all their resources should go into it.

This misconception is a bad idea, you should have a small fleet of ships at your disposal each tuned towards one purpose. A pilot flying missions for corporations will have a primary combat ship for dealing with the missions, a dedicated salvage ship for clearing the loot from the battlefield, an industrial ship with a large cargo hold for moving the loot to a market hub for selling. Industrialists will have small, fast shuttles for moving blueprints about, and larger ships for moving materials and perhaps a dedicated mining vessel for harvesting the materials needed. PVP pilots will have a whole hangar full of ships for different purposes - tacklers, snipers, covert ops - and spares for when they lose them.

Being too focussed on one ship is a bad idea, because it's very likely that one day you might lose it, and if you've poured every penny into it then you'll have very little to fall back on. Every day there's players who profess that they're going to quit because they just lost their prized ship, and while it sucks it's a fact of life in the game. Myself I've lost over a billion isk in ships, and I keep coming back, frequently I come back in time to lose another ship to the same enemies.

There's a saying "Don't Fly What You Can't Afford To Lose" - ignore this advice at your own peril.

But, more insidious is the fact that pilots get so attached to their ships early on in the game that they become very risk averse, they carry with them the fear of the dangers in low-sec and 0.0 and choose to remain in hi-sec under the limited protection of Concord.

The new Advanced Combat tutorials introduced in Dominion have a couple of missions where you cannot complete the missions unless you lose your ship, best of all they give you some ships for these very tasks - be sure to insure them for some extra cash :)