They are important at cocktail parties.

They’re not that important until you get one that sucks at their job.

Depends on how long they stay and whether faculty are behind their vision. If not, it gets ugly. Some starchitects are appointed for short vanity terms to boost rankings and invite their famous friends to speak.

They are hugely important for fundraising - Bob Stern's Yale tenure was a powerhouse in that regard. Some come with a strong pedagogical agenda like Sarah Whiting when she introduced industry partnerships and training at Rice. Amale Andros also had a big hand in shaking up GSAPP's curriculum and structure when she came on board.

The thing to go in knowing is that they don't usually stay Dean for very long, so the chances that the one you start with is the one who will be there by the time you finish are 50/50 at best. Factoring them heavily into decisions on where to attend invariably leads to some threads from hugely disappointed newly admitted students every June and July when some schools' Deans announce their departures before those students even arrived. When one decides to leave it usually results in somewhere between 1 and 4 semesters of an Interim Dean while a search is conducted, so a large % of all students spend a large part of their academic career in the midst of that process of change.   Nationwide an architecture dean's average run is a little under 6 years.  There are some who last twice that or even longer, but there are also a lot who barely stick it out 3 academic years, and a few who don't last a year.  Some universities have set terms of only 3 or 5 years, and policies that don't allow multiple terms, so in those cases you're nearly guaranteed a Dean search during your time there.

In hindsight I'd say that one of the Deans of one of the schools I attended was a strong role model for me, so was critically important, while the others ranged from benign bumbling administrator to power-tripping temporary fill-in, none of whom were really disastrous, but also weren't in any way directly important to my education in the long-run.

I could barely tell you who my dean was. I know there was a search during my first years there, and that in the later years a lot of the arch. faculty were disappointed in him. I think the issue was that he emphasized the other departments (art, l.arch., etc.) in the college rather than architecture and [sarcasm] we all know that architecture is the most important [/sarcasm].

In academia, the Dean of a school of architecture is definitely important and they will have an influence on the program within the school. Most students may not interact much with the Dean, but the behind the scenes functions of the person in the position are important. Don't forget that there are also many other staff and faculty involved in a program's direction though. It's a group effort.

Check out our Deans List series on Archinect if you want to hear what Deans have to say about the work they do. You'll learn a ton.