When there comes the time to improvise, let's say on a "twelve bar blues" in E, and let's take the following progression you play the E chord in the first four bars, then you go to A in the next 2 bars... as in the following:

I    II     III     IV     V   VI   VII    VIII     IX     X     XI      XII
E    E      E      E      A   A     E        E       B      A      E       E 


Can I keep playing the E scale througout all the bars?
Otherwise, What scale should I use?
How can I make the solo sound cool???

well... the answer to the first question is: Yes.
the answer to the second question is: The ones that sound good.
the ansewr to the third question is: practice and listen to other people.

you can in fact use the E minor pentatonic scale... otherwise known as G major pentatonic, and you can use it over the entire progression, yes, and it will sound fine, interestingly enough, even though the scale has notes which seem to "clash" with the chords. The fact is... all those chords, in the blues that is, are Dominant. This means they've got a major third and minor seventh, as far as intervals go. The E minor pentatonic has a minor third, which would, on the outside, seem to clash with the major third in the chord. This is not so, however, because the resultant harmony is known as an "altered dominant" type of harmony (note for the purists this is not to be confused with a defacto Alt chord, which is a similar but different beast). Technically speaking it's a Dominant-7-Sharp-9 chord, if you can wrap your head around that, and it is in fact the essence of what "the blues" sounds like. So go ahead and solo over the whole thing in E minor pentatonic, but don't be afraid to "step outside the changes" once in a while. For example... a tritone substitution can hop you over to a Bb minor pentatonic and, if you do it just right, it'll sound pretty freakin cool. ok... have fun... if you have no idea what i just said, go take some theory lessons.

... my advice - mess around and try things.  the only rule in music is that there are no rules.  just remember that if you get a little lost, you can always rely on the minor pentatonic scale of the key (eg E minor pentatonic in the example you gave) to get you out of trouble if you need it to.

I would suggest using an e minor blues scale over the "e" chord, an a major blues scale over the "a" chord and either major or minor blues scales, or b dominant arpeggio over the "b' chord.  Also try sticking on notes that are common tones between the different chords.  For example play the hell out of an e note anywhere on your guitar and keep playing it as the prgression shifts between the e and a chords.  It's what's known as a "pedal" (like holding down the pedal on a piano to get sustain) and usually rocks harder than playing a million notes a second.  One last thing i'll mention, like everyone else has, is don't be afraid to play outside of the scale.  It really doesn't matter what notes you're playing as long as you convince your audience that you mean to play it.  Anyways, music is really more about rythym than the notes you play, so if you play the hell out of a dissonant note with a cool rythym and resolve it to a note in the scale it will sound like a beautiful catastrophy.

Although I don't play guitar, I wouldn't necessarily recommend that.  If I saw someone do that I would probably be more likely to assume that they just can't tell that it sounds bad.  (Assuming it was a mistake that was noticeably incorrect - if you play an incorrect note that still sounds good, then yea, that's cool.)

depends on the genre - jazz or blues: you can litterally get away with ANYTHING

I say dont think about it to much. Your way into depth. Just record a progression and Jam away!!!!

OK, this is an excellent question for a beginner, and for a long time, I could not have answered much beyond "play a E minor pentatonic, or E (minor) blues scale."
After some study, I discovered B.B. King used E mixolydian as well as the E (minor) blues scales.  He mixes the two. 

I've listened to others, such as Little Charlie (of Little Charlie and the NightCats fame - a flat out amazing blues guitarist) and by transcribing his solos, realized he uses a lot of chromatic (passing) notes also.   He also uses E mixolydian and E blues scales.  Now by combining these three, he uses most of the 12 notes of our western music system.

So the final answer is what B.B. King said.  It went something like this: "know all the notes and play the ones that sound right to you." 

But that's not much help.  What is, I think, is to learn some blues licks, to get a feel for what sounds right.  There are hundreds of books out there with blues licks and blues method and all that.  I'd suggest buying some.  Most of them come with CDs these days.

When/if you get serious, start learning some theory. 
I'd start with learning chord tones.  example: E7 chord = (1,3,5,flat-7) E, G#(sharp), B for example.
Then scales. example: E minor blues = (1,3,4,flat-5,5,flat-7) = E, G, A, B-flat, B, D

And have fun with it.

One thing that you could do is while hitting E, play a second note like you would play just a diatonic cord. If your playing in E-pentatonic, naturally, G will sound good(being that it's the minor tone), B will likewise(being a perfect 5th) as will d and a. Then miander a little bit with those notes and find what you like best. The thing about the blues scale is that all of it's pitches sound good while soloing. So then, the only thing that you have to worry about is your own style. That rests entirely on you. That's the beauty and also the down fall of that scale, it's good to learn with, but a lot of guitarists don't move beyond it. Try not to fall under the later! Kudos!

Theory is interesting for solo, but that's poor to think a build a solo, you shall improvise, don't try to learn a solo!!

Here are my tips. I'm not a professional, but I do not think I'm totally wrong :

At first, learn your 5 pentatonic scales to know the whole notes you can play on your solo. That's the base and it can not work if you don't know the entire scale. Try to go in trebles as you play your solo, but don't forget to play the middle or bass notes of the scale.

Try to play on one scale and progress by "jumping" on an another scale.

Make some bends, slides, hammers/pulls-off to give life and energy to your solo.

Try some exercises as broken scales, octaved-scale and quinted(?)-scales.

Last tip : Experiment!!!!!!
By searching how making your solos and trying different things, you will build up your own style and on that moment, it will sound cool

When I solo, I try to create a sort of tension by staying off the root notes for a while, and, say, picking three or four notes and playing different combinations of them in different rhythms. For example, on E, I might choose F#, G#, A, and C. I might play around these, throw in the occasional D, and then on a switch to the A chord, might land finally on the E, and then use three other notes in addition to this to create new sections. Use different notes each time, and work around the chord instead of the scale, such as flatting the two to make a quasi-Phrygian scale.

i can honestly say that not 6 months ago i was asking myself the exact same question, how to make a solo sound cool etc.

there are a few things i've realized since then:

1. it is more about ear training than about strategically playing different scales over different chords.

2. sing your guitar solo over your chords then copy it on a guitar, if you can sing a badass guitar solo it will sound even better through a guitar.

3. think about visualizing your scale notes as a relationship with the root note, minor 3rd, minor 7th, 4th, etc.  focus on how they feel compared with the root note and give that feeling the label 'minor 3rd' etc in your head.  then add on all the other notes tend to sing to make your own scale.

when i was experimenting soloing before by pure random playing of scale notes, i would often resolve to notes that didn't feel right to me.  or resolve to the same notes over and over so the solo became stagnant.  i'm not sure if your problems are the same as mine but anyway...

well, those are very common problems
in fact I think those are absolutely the most common problems.

any one else with good suggestions on how to fix those commons problems?

If you're just beginning to play guitar solos I'd recommend to start with the A format insted of an E.
The A pentatonic has an easier position on the guitar neck than the E one. Just at the beginning of course.
Even though the A pentatonic scales notes are:  A - C - D - E - G - A
You could try that scale for a while and enjoy it a lot, the position is really easy (the root note A on the 5th fret of the 6th string).
Later on you can try the "blues" scale which is the actual pentatonic with some chromatic or passing notes, all the notes you can play on the first position of the A pentatonic are:
A - B - C - C# - D - D# - E - G - A -  C - C# - D - D# - E - F# - G - A - B - C

You'll need to find the right positions for your fingers as I don't have a TAB staff in here.
And more importantly feel the guitar.

errr... careful there with your terminology... i've gotta be a stickler and point out that you're talking about the A minor pentatonic... when you just say A pentatonic that REALLY means the A major pentatonic... if/when the words "major" or "minor" are not explicitly said, then it's major... and they are very different beasts...

anyway, just wanted to point that out... but yes your suggestion(s) are still perfectly fine... so listen up yall... start out on the A minor pentatonic first rather than the E minor pentatonic... yes I know it's a mouthfull but if you use it then there won't be any confusion