I've found that algorithms are one of those things that doesn't come up often in your daily work, but when you need them, you really need them, and otherwise you'll end up delivering a substandard product. It's very much like Joel Spolsky article on hitting the high notes:

http://www.joelonsoftware.com/articles/HighNotes.html

I've found that in my work, a tricky algorithmic problem comes up on average about once a month. It's a tiny fraction of the total work I do - but if I couldn't solve algorithmic problems, then there are whole projects that I simply couldn't tackle. We'd either do something substandard for users, or we'd throw bodies at the problem (which still happens a lot, unfortunately), or they'd need to bring in someone else to do my job.

Moreover, I've found that there's a cultural shift that happens when enough people are familiar with algorithm design within a company. A lot of other places I've worked are basically "Make the user fill out a form, dump it in a database, format it for display." When a significant fraction of your employees are capable of hitting the high notes, this becomes "Make the user interact with your system in the manner they're most comfortable with, extract meaning out of their ordinary behavior, compute interesting results, and show it to them." The complexity moves from the user to the software, and as a result, users would rather use your software. There are whole subsystems within Google Search - synonyms, spelling, refinements, authorship, snippets, ranking, translate, voice search, etc. - that would never have happened if there weren't a critical mass of people willing to dive into difficult problems.