Some good comments - to recap and add my own twist:
When the guitar is playing bar chords, the main notes are 1-5-8 (F-C-F, etc.), an octave with a fifth in the middle. Keyboardists are tempted to throw in a third. DON'T! Two reasons - 1) the guitar usually does not play the third; and 2) if the guitarist is wrong picking major or minor (keyboardists are too smart to make that mistake), you don't highlight it by clashing with them. Or if you're a slumming keyboardist, it saves you from having to instantly figure out "major or minor?" over and over on the fly. This is particularly useful when playing with people you have not rehearsed with. It is simply not required to play EVERY note that the guitar is handling, and it's often better not to.
When filling in guitar parts with keyboards, you have a lot of choices. You can pick sounds that have attacks (Rhodes, acoustic piano, clavinet, . . . ) and sounds that don't (organs, string pads, fat sawtooth a la "Jump"). You have bright, prominent sounds (clavinet, sawtooth, bright piano, Farfisa organ, full Hammond w/ chorus/Leslie) or smoother sounds that just add weight (Rhodes, Wurlitzer, square wave, 888000000 Hammond w/ no chorus/Leslie). You can duplicate the rhythm of the guitars, you can do a counter rhythm, or you can just play power chords. You can play in the same range as the guitar or bass, which makes a big sound and conceals the addition of keyboard better, or you can get a less muddy sound and broader soundscape by picking your own range to play in. When replacing a guitar, pick a sound that has a similar attack envelope - replace strummed guitars with percussive attack sounds, replace power chords with sustained, flatter attack envelope sounds.
On a similar note, the best thing you can do is pick when NOT to play. In pop music, the chorus is almost always "bigger" than the verse. Try just playing on the chorus, or using a thicker sound on the chorus. The myth is that "more is better". The truth is, "contrast is more interesting". Not playing on verses is the easiest way to achieve that. Except that you have to figure out what to do so you don't look awkward while not playing.
Solos - keyboardists learn major and sometimes minor scales in piano lessons. Then they apply that to solos. NO! Learn to play like guitarists. Use blues and pentatonic scales, learn Dorian and Mixolydian modes. Set your pitch bend wheel to a whole step to a minor third for string bends (bend up), or you can give it more range for whammy bars (bend down). Pitch bending up is the equivalent of a guitarist bending a string. The string will typically break if it bends much farther than a minor third, so don't exceed the guitar's limitations. Listen to which notes in the scale guitarists like to bend, and how much. This is not a hard and fast rule, but bending from one note in a scale to the next is often a safe bet. Here's a tip you don't see everywhere - combine Mixolydian and major blues, or Dorian and minor blues. In other words, add flat 3 to your Mixolydian, and add flat 5 to your Dorian. This saves you the mental exertion of hopping back and forth between a mode and a scale. In bluesy contexts, try out Dorian and minor blues scales.
Articulation - I have a hard time convincing some guitarists of this, but I am most successful adding to or replacing guitar parts if my articulation is spot on. I place that BEFORE selecting the patch that comes closest to a particular guitar part's tone. I usually forsake the "Wall of Sound Marshall" patch for piano or organ because they tend to be more responsive (in a natural, not "programmed" way) and can often achieve the guitar's "musical purpose" in the song better than a sampled/modelled guitar patch. So, your job is to pick a patch with an attack envelope and playing response that allows you to best duplicate the job that the guitar is doing. Is your stacatto similar in length and sharpness of the guitar's? Does the tail of your sustained notes approximate the guitar's?
Conclusion - start out with smoother, less obtrusive sounds and accompaniments, and then grow into more prominent sounds and more active playing as you grow in your sense of what works and what your band will tolerate. The point is to make them sound better, not to bow in worship to your rig and playing prowess.