The bowsprit is found at the very front of the ship, usually a long plank or spar to which the forestays are attatched, with the bobstay running down beneath it to the keel. It's the place to stand if you're going to spread your arms wide and do Kate Winslet impressions, a la Titanic.
On the ketch I've sailed on, it's by far the best and most exciting place to sit. The boat pivots in the middle, so sitting at the furthest point away from the center means that every motion is amplified under you, you feel every wave hit, and every rise and fall of the boat's movement.
If the sea is especially choppy then the bowsprit spends most of its time being dunked under the water, which can be either a frightening or exhilarating experience depending on the weather. Trying attatch the jib sail to the forestay when you're up to your neck in water and being pounded by 10 foot waves is a very unique experience!
The bowsprit is a place to be to meditate on the days happenings. If you sit right at the front and lean forward, then all you hear is the silence of the sea. It does feel like flying, watching the shadow of the boat moving over the waves beside you. If you lean back, then the rushing, gushing, chuckling noise of the bow wave can be heard breaking behind you, occaisionally splashing you if the boat catches a wave at the wrong angle. Tiny rainbows chase your toes from the spray on a sunny day, and you can feel the thrumming of the wind in the wires and the wood during a storm.
My favourite position is to lie across the bowsprit, with my toes and fingers hanging down towards the water, so every time the boat dips you nearly, oh so nearly, touch the ocean. (Though this is far better on the cool, clear blue waters of the Atlantic, rather than the scummy, murky inshore waters of the UK!)