How much of my time is spent on algorithmic problems? Not as nearly as much as I would like!
I once wanted to stay away from web development because I knew a lot of it would be boring stuff like learning to work around browser bugs (which change with every generation of browsers, rendering your previous learning useless), rather than the mathematical/algorithmic mind puzzles which I really enjoy. I gave in because there's so much work available (and I found some clients who pay really well).
I think having experience working on both low-level embedded software and algorithmically intensive software (natural language processing, etc) gives me some advantage as a web developer. When the need to devise an algorithm or do something else hard-core comes up (which it does from time to time), I take it on with pleasure rather than shrinking back in fear. Or if I find a bug in my platform, I can drop down into the C source, figure it out, and submit a fix to the maintainers, rather than waiting for someone else to help.