Four spacecraft (two Pioneers, two Voyagers) are currently leaving the solar system. Five, if you count New Horizons which is on its way to a flyby of Pluto.

None of them are leaving exactly in the plane of the planets, but none of them are leaving exactly perpendicular to the plane either. They are leaving at various angles to the plane, based on their mission and their last flyby of one of the large outer planets. Their paths were set up to take advantage of the location of specific objects, like moons, during their flybys.

That said, space is big. Really big. The aforementioned craft, while they are leaving our solar system, are for all intents and purposes still within the Sun's influence and it will be tens of thousands or hundreds of thousands of years before they pass somewhere in the neighborhood of another star.

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"Arrrgh, the laws of physics be a harsh mistress!" -- Bender