Compared to the value of having coders on a team, how do designers stack up? Is it common to have a designer on board, or to just a design firm? Also, have the majority of teams accepted to YC had designers on the team, and if not, what have they done? Perhaps pg can best answer that last one.
Thanks.
So, early stage, it is valuable--maybe not valuable enough to have one as a full partner with equal equity, but maybe.
The reason I say possibly not is because I know many of the "rock star" designers from YC companies now, and at least a few aren't feeling very important to the process or involved in the day-to-day development (and some have packed up and gone home). If you can't foresee significant design work throughout a long period of time, maybe an equal partner designer isn't the way to go.
So, great design is a huge value. It's up to you to decide if it is worth an equal stake (it's almost certainly worth some equity, if you can get someone good to work for equity and don't have the 10-15k it'll take to hire a good designer for a couple of weeks), and whether they'll be twiddling their thumbs in six months.
As Harj said, a designing hacker (even if the hacking is fair to middling--if the design skill is really strong) is a champ worth her weight in gold.