Warm-Up Exercises
Petrucci Chords
see Advanced Technique Exercises#Petrucci Chords
Chromatic Scale
Scales
Practicing various ascending and descending scales (be sure to play through the transitions from ascending to descending and descending to ascending) is always a good idea, especially the scales and positions you are likely to perform. You can find a giant reference of all the common scales at Ref: Common Scales, and full scale maps across the entire fretboard for the major and minor scales at Ref: Scale Fret Maps for all Major/Natural Minor Keys w/ CAGED breakdown.
For lots of exercises, see Common Scale Exercises.
Arpeggios
Just like scales, arpeggios are good exercise - focus on the ones you'll tend to use. Or at least the ones that give you fingers a good work out. There is reference for all the CAGED major and minor triads. It should be somewhat simple to alter these to fit other chord types, which are referenced at Ref: Mega List of Chord Fingerings/Voicings. For example, adding the minor 7th of dominant major/minor chords.
Rhythm
The best way to warm-up for rhythm is to play to a metronome or a good drummer. The first thing to get down is consistency, so all your notes fall on the beats and have equal duration. Metallica used to warm up by simply chugging palm mutes on the open low E string for a good 5-10 minutes. It seems simple until you try it.
1 n 2 n 3 n 4 n 1 n 2 n 3 n 4 n x100
pm pm pm pm pm pm pm pm pm pm pm pm pm pm pm pm
E-|:0--0--0--0--0--0--0--0-|0--0--0--0--0--0--0--0-:|
Practice on at least 4 different speeds, with an extreme slow and a fast speed that is close to your maximum. Practice with all downstrokes, all upstrokes, and strict alternate picking. Obviously, the straight down or upstroke exercises will require a slower speed than the alternate picking. Also try different strings.
This same exercise works for strummed chords, although you'll likely need to reduce the relative speeds. Start by keeping the left hand constant, holding the same chord throughout.
Playing the same note or chord over and over is easy to get a consistent rhythm. Trying to keep that rhythm with runs or riffs or chord changes is another story. Once you establish a good right hand using the above exercise, you have to lock it in. Don't ever let your right hand wait to catch up with the left. If the left hand is slow to fret the notes, play them uncleanly. Throwing off your rhythm might sound ok playing in the bedroom but becomes painfully obvious in a band or recording context. Even playing solo, hearing it played back that inconsistent rhythm sounds pretty terrible. Unclean playing is also noticeably bad, but sounds less amateur. And its easy to get in the habit of sacrificing rhythm to attain synchronicity, which then becomes difficult to break. The other way around is going to be more noticeable to you and annoying and forces you to make the left hand sync to the right hand.
The kind of playing to get a good warm-up for rhythm will depend on the individual and the type of playing you perform. If you are a rhythm player, it may make sense to alternate between two strings or power chords or full chord changes. If you are a lead player, playing various scales ascending and descending, as well as arpeggios or advanced techniques like tapping and sweeps makes more sense.
The key thing is when you're jamming or playing along to your favorite song or trying to record a part, you may notice some riffs or chord changes or rhythms that seem impossible to nail. Make a mental or written log of these things, identify the specific parts of the licks or riffs or changes are giving you trouble, and try to break down why it's difficult. This will let you develop your own exercises that consist nearly entirely of such. It's helpful to alternate between sections of these parts and just chugging on single notes or a static chords like above.
Another thing to practice is throwing in accents. Start by putting accents on the beats:
1 n 2 n 3 n 4 n 1 n 2 n 3 n 4 n
> > > > > > > >
E-|:0--0--0--0--0--0--0--0-|0--0--0--0--0--0--0--0-:|
1 tr lt 2 tr lt 3 tr lt 4 tr lt
> > > >
E-|:0--0--0--0--0--0--0--0--0--0--0--0--:|
tr lt = trip let; so 1 trip let 2 trip let ... etc.
1 u n u 2 u n u 3 u n u 4 u n u
> > > >
E-|:0--0--0--0--0--0--0--0--0--0--0--0--0--0--0--0-:|
1 t l n t l 2 t l n t l 3 t l n t l 4 t l n t l
> > > >
E-|:0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-:|
t l = trip let; so 1 trip let and trip let ... etc.
It may be easier to just say 1 n uh and n uh 2 n uh and n uh ... etc.
The faster the tempo, the harder it is to work those accents in. But they really help you keep a consistent rhythm - you know every 2, 3, 4, or 6 notes you should be making an accented downstroke on the beat. It's easy to hear when and in which direction your rhythm is falling off and make the correction. A consistent rhythm demands control and accents demand more control than static dynamics. That makes this a great warm-up.
Then you try trickier accent patterns, where accents alternate between downstrokes and upstrokes.
1 n 2 n 3 n 4 n 1 n 2 n 3 n 4 n
> > > > > >
E-|:0--0--0--0--0--0--0--0-|0--0--0--0--0--0--0--0-:|
1 n 2 n 3 n 4 n 1 n 2 n 3 n 4 n
> > > > > >
E-|:0--0--0--0--0--0--0--0-|0--0--0--0--0--0--0--0-:|
1 n 2 n 3 n 4 n 1 n 2 n 3 n 4 n
> > > > > > >
E-|:0--0--0--0--0--0--0--0-|0--0--0--0--0--0--0--0-:|
1 n 2 n 3 n 4 n 1 n 2 n 3 n 4 n
> > > > > > > > > >
E-|:0--0--0--0--0--0--0--0-|0--0--0--0--0--0--0--0-:|
Finger-Stretching
Similar to the Petrucci Chords exercise above, we make a chord shape with each finger on adjacent frets. Each time you strum the chord, you move one of the fingers down one fret.
-12\11-11-11-11\10-10-10-10-...2\1-1-1-1- -13-13\12-12-12-12\11-11-11-...3-3\2-2-2- -14-14-14\13-13-13-13\12-12-...4-4-4\3-3- -15-15-15-15\14-14-14-14\13-...5-5-5-5\4-
This exercise is great, because as you descend down each fret at a time, the exercise gets more and more difficult. It forces you to stretch between each pair of adjacent fingers, which really helps limber up your hands to make complex chord shapes and work through exotic scales all over the fretboard.
This will get insanely difficult quickly. Don't push yourself into injury - if you feel intense pain, stop immediately. Don't try to get through it quickly either. Hold each chord and let your fingers muscles accept the stretch.
Here's another one focusing on the index finger and pinky. Be sure to keep the index finger fretted at all times forcing you to stretch rather than bouncing back and forth.
-17-12-16-11-15-10-...-10-5-9-4-8-3 p i p i p i p i p i p i
This follows the same premise of getting more and more difficult as you descend, but is focused on more traditional stretches. The same guidelines apply as above.
It can also be done using ring and index, middle and index, pinky and middle, and ring and middle, but you'll have to use a smaller stretch to be able to do it.