I have always been able to find internet without too much hassle, except for Saturdays and Sundays. It has been my experience, like Sil's, that the number of internet cafes is dwindling, but they were only in the bigger cities anyway, and those cities all have libraries with lots of machines. In smaller places, I frequently found internet either in the casa de cultura, ayuntamiento, hogar del pensionista, job training places, or in ciber places funded by the regional government. In some places, I found a library next door to a regional government ciber office, both of which had lots of machines. Many of those sites close for hours in the afternoon, though, which is prime pilgrim time.
On the more remote caminios, like the Invierno and the Madrid, internet was really a life saver for me, as it was the only way I stayed in touch with my family, and it gave me access to newspapers, this forum, and email -- all of which were very welcome distractions in small places. I walked on the Vdlp last year with someone who had an iphone, and she had endless hassles trying to connect via wifi, but I am sure that situation is changing quickly.
I share the concerns about "how connected" we want to be, but having access to it gives me gret peace of mind. I surely hope that computers in public places don't go the way of the pay phone!
Buen camino, Laurie
p.s. Claire, your mention of Salamanca reminded me that when I was there, a friend went to the tourist office to ask about internet, and the employee sent her halfway across the city to find a ciber-cafe, even though the public library, with at least 20 machines, was right around the corner.