Here are two great chromatic scale exercises to work on your technique, tone and time/rhythms.
Every improviser should have this scale at their command : it is like our "musical alphabet".
I often get asked by students : "...I know scales and stuff, but how can I add more chromaticism to my lines? How can I connect everything with half-steps?"
My answer is : well, practice the chromatic scale first and all this stuff will soon become available to "glue" your melodic lines together.
Chroma means color in Greek. This scale encompass every color (thus every one of the 12 notes available on our Western musical instruments.)
The twelve notes, starting on C :
(ascending) C C# D D# E F F# G G# A A# B
(descending) C B Bb A Ab G Gb F E Eb D Db
In fact, the entire scale is easily played on a single guitar string! All you have to do is to play each consecutive frets, up or down.
The scope of this article being technical exercises, we'll look at two ways of organizing this scale on the fretboard : vertical and diagonal.
This exercise "fits" the chromatic scale in a guitar friendly format : four notes on each string. It has a vertical direction on the fingerboard (similar to position playing) and a two octave range.
Play this one in strict alternate picking, picking each new string like this : down - up - down - up.
This exercise is harder than the previous one : it has six notes on each string. Its direction is diagonal thus spawning on three octaves. Look up this diagonal playing article if you need more info.
Make sure your two external fingers (index and pinky aka 1 and 4) cover two notes each! The fingering pattern is the same on each string :
index stretch - index - middle - ring - pinky - pinky slide ... or ... 1 (stretch) - 1 - 2 - 3 - 4 - 4 (stretch)
Also play this one in strict alternate picking.
Here's the "4 per string" version played in groups of three notes (accents are sounded with the pick) :

Here's the "6 per string" played in in 4/4(real nice!) :

This process is described in a great book titled Forward Motion.
Check it out!
Jazz Guitar Chords and Jazz Harmony