WARNING: Long AndyR post ahead :lol:
Sorry folks :roll:
Even some hardcore jazzers don't bother with modes, they look at everything chordally. They may play something that someone would call a mode but they are arriving at it from a different place with a different mindset.
This stuck out when I was reading through.
I actually look at everything chordally. I think in terms of melody lines (vocals, solos, riffs even) modifying the harmony of the underlying (or implied chord). So if the chord is a C, and I sing or play a D, the chord is now a Csus9 (or 2 if you want!). If you do the blues dunga-dunga riff with the pinky finger, you're adding a 6th with the pincky, so I think in terms (if the chord is E) of an alternating E and E6 sequence.
All of my lead playing is based on these principles. First off, what's in the chord - I can play any of those safely, but on their own you'll be hard pressed to sound interesting. So you add the groovy notes as passing notes - 4ths, 6ths, 7ths etc... plus any note you fancy trying. I also tend to pay attention what key the song is in, what the next chord is, and whether the song's key is major or minor (that's where the modes actually provide the theory to "explain" it all)- you tend not to change the key of the melody line everytime the chord changes (unless you want to, that is!), so the notes you can safely play over an A chord in the key of A are slightly different than the ones you play over A in the key of D.
To kick this off originally, I did learn what turned out to be the minor pentatonic thing - but I found it myself. When I started learning to improvise "blues" lines, I recorded a bunch of twelve bar in E. Then I experimented with all the notes in the first 3 or 4 frets to find out which ones seem to work and sound "solo-like" when played in little phrases.
I can still remember the ones I found - E, F#, G, A, Bb, B, (C), D - the C is in brackets because I liked it a lot but it seemed you had to go careful about when you used it, C# was an option too. There was no possibility of bending strings on this acoustic, so that's probably why I had Bb in the list.
Then... I got a white crayon and marked the fretboard with every occurence I could find (and reach) of these 8 notes.
I spent a couple of weeks (I was 16 or 17) fiddling around with this looking for ways to get from note to note easily, finding little phrases that sounded good to me. I ended up finding a position at the nut, using frets 1, 2 and 3 (and therefore duplicated at the 12th fret), and another at the 7th fret with different shapes. It was obvious to me you just moved these up and down the neck if the key changed. I got away with just this lot for about 5-7 years and loads of gigs :lol:
I could use more notes in the scale if it wasn't blues - I was already comfortable with major and minor scales, and the white crayon exercise had taught me where a bunch of notes were on the fretboard, so my brain soon learnt the rest.
It took me years to figure out how to be comfortable with Major pentatonic - you kind of need that for Rock and Roll tunes and Country (which was cropping up), but I just fluffed my way through it - if the song's in A, play the shapes you know for F# minor pentatonic, no-one seems to notice the difference! :lol: (Sh1t! I just realised I still do this 20-odd years later).
Meanwhile I was writing and arranging songs - so chords and harmony were always in my mind. Somewhere I read that chords are just the notes of scales stacked on top of each other and vice versa... so that encouraged me to pick the side I understood - harmony - and do it all from there.
The modes, which I don't find that helpful myself, do actually describe all this stuff - but I find it so much easier if I can hear something I like first and then get told why it works. When I looked into the modes (I was about 19) it was all a bit dry and mathematic, I liked it for that reason, but I couldn't hear no music coming out of the theory!!
I think you're absolutely right, Andy.... but remember not everyone has ears as good as yours, so learning a few things by rote can possibly help. Sometimes. 
Hopefully some of the waffle above shows that I did actually learn it "by rote" - it's just that I picked the notes that I wanted to learn myself :lol:
I have a real feeling that I can improvise at will partly because of this. I wanted to learn how to "talk" with melodies and chords, so I went by sounds and what felt good. Once you've learnt a few phrases and tricks of your own you start hearing the relationship to other people's phrases, you understand what it is they're doing, and you can nick theirs as well. Other guys I knew at the time were getting lessons or whatever (I don't remember modes being the "in thing" they became later, though), and to my amazement I've found that some of them still can't improvise, even though they'd like to be able to. They know far more academic music theory than I do, but if we're chugging along on a chord, they're not able to suggest what a groovy next chord might be (so we're stuck in twelve-bar land until I take over and start yelling interesting chord changes at them :lol:).
EDIT: Lezard said it all much more succinctly while I was rambling. Especially this:
I find it easier and quicker to play from the root note and add the intervals I want or play altered and extended arpeggios and any other chromatic bullshiteeeeeeeeeee that comes to mind.
And as has been said, for the orignal question, you don't really need modes to solo.
Major and minor scales, pentatonics and chord tones should be fine untill you decide you want to try something else.
and learning intervals couldn't hurt either.
