Generic Bed
    The basic bed would be a prepared planting area for flowers, vegetables, shrubs, and/or trees.  A soil test can be done to see if any amendments are needed so they can be worked into the soil prior to planting.  For trees and shrubs doing a bed rather than a hole helps them to become established sooner plus allows annuals to be easily planted around them to fill the space while the shrubs reach maturity rather than overplant the shrubs, which will result in the shrubs becoming overgrown.
 
Geometrical Designs
    Geometrical designs are only limited by what can be drawn and then reproduced on the ground within the scale of the landscape and budget.  This may involve the shape of the bed such as elliptical, or patterns using plants such as a a knot garden.  Geometry is also used for garden paths such as labyrinths, water features, and orchards.
    A recognizable example geometrical designs is crop circles, but a better way to produce a similar effect would be using different plants rather than being needlessly destructive.
 
Raised Beds
    Short of a hanging garden the raised bed is the ultimate type of garden bed.  Advantages to a raised bed can include being able to work in the bed while sitting on the retaining wall rather than bending or stooping, and having control over the soil used to fill the bed so that it will be idea for the plants that you want to grow.
    A terraced rock garden is a variety of a raised bed that would be suitable for sloped and/or rocky lots.  Water is important for most raised beds especially if there is little or no soil below the raised bed that contains moisture capable of reaching roots through capillary action as would be the case when built over a shallow rock.  In such a case it would also be better to select plants that can tolerate such conditions.