From a stylistic point of view, 'personal', 'flexible' and/or 'improvisatory' are my general conception of the prelude. I'd like to share the rationale behind such a conception by tracing back to the Renaissance and Baroque periods, when very early (notated) preludes appeared and were being developed.
According to The Harvard Dictionary of Music, an idiomatic virtuosity, rhythmic freedom and loose thematic construction are the noticeable qualities of the prelude. The tiento, toccata, ricercar, fantasia, arpiggiata, tastata, entrada are all virtually identical in style and function to the prelude.
The very early examples of the preludes are thought to be freely composed small improvisatory pieces for organ, lute and other Renaissance string instruments, and were used as an introduction to the main works or a warming up.
In the 17th century, French lutenists and harpsichordists developed the 'unmeasured prelude', which is a prelude with no time signature, no bar lines, and often with very few note-value indications. As rhythmic interpretation is mainly left to the performer, the improvisatory element is very noticeable.
An example of unmeasured preludes for lute by Nicolas Bouvier (1638).
An example of Louis Couperin's unique notation for unmeasured preludes.
Here are two samples of unmeasured prelude and fantasy outside France.
An excerpt from Prelude from Sonata No.3 in G minor by a German composer Silvius Leopold Weiss (1687–1750).
The first half of the famous Fantasia in C minor, as known as Fantasia in E minor for guitarists.
Silvius Leopold Weiss: Fantasia in E minor (modern guitar)