Intro: Earth's Gravitational Field
Example: gravitational field around more-or-less spherically symmetric object (Earth is pretty close). The vector gravitational field around this object is the collection of all these vector g's, all pointing radially inward towards the object.

 

Electric Field around a point charge
Single POSITIVE point charge: Field lines streaming radially OUTWARD	Single NEGATIVE point charge: Field lines streaming radially INWARD
Electric Field around a PAIR of point charges
Field around an Electric Dipole	Field around a pair of + charges
Another 'format' (called a 'streamline' display) to show electric (and other) fields emphasizes the direction of the field but doesn't show the changing magnitude.
Field around TWO + charges	Field around TWO - charges