Another my "just for fun" small program. It was made as simple as possible (in reasonable borders of course) and works completely on client-side browser. Algorithm uses finite-state machine to calculate possible cells to paint and eats, as I suppose, O(n2) machine time (and what do you want from NP-complete problem?). In addition there is brute-force search function in order if puzzle has no obvious solve steps but herewith has single solution. On huge grids solver runs deadly slow.
Eventually I'm a big fan of nonograms. My Android phone has CrossMe installed, and I play it often, especially if I have to wait for my wife while shoping =)
By the way, first attempt to create such solver was in 2000. We were first-year students and compete each other whose algo will solve puzzle from newspaper faster. But we even did not know about finite-state machines at that moment. I left my Intel 80486 computer to calculate grid for whole night, and after eight hours it was still unsolved =) Well, I will show my current algorithm to students after all =))
UPDATE. There is completely awesome survey about nonogram solvers and large collection of online and offline solvers and puzzles by Jan Wolter: http://webpbn.com/survey. I think everyone who interesting in nonograms will satisfied totally there. In additional, Jan presents list of puzzle exporters: http://webpbn.com/export.cgi.
UPDATE2. Great, google says this is the most popular solver we have for now: https://www.google.ru/#newwindow=1&q=online+nonogram+solver
For children getting upset with the solver: remember, a computer is not a human, it can't understand what the thing it's solving. If you have meet bad luck first time, try to use your intuition and help the solver checking/unchecking squares, and then let the solver has another try.