What's the best UI for entering date of birth?

If your goal is to make sure "the user won't be confused at all," I think this is the best option.

I wouldn't recommend a datepicker for date of birth. First you have to browse to the year (click, click, click…), then to the month (click some more), and then find and click the tiny number on a grid.

Datepickers are useful when you don't know the exact date off the top of your head, e.g. you're planning a trip for the second week of February.

Whilst this is a very old question, it is so important in getting a date of birth input correct, especially in a registration form.

I think no one has done this better than the google accounts sign up:

Select the month first from a select box and manually type in the date and year. Simple.

Easy to validate. Easy for users to get right. No scrolling back the years in a select box from 1900-the present year. No need to update a 'day' select box based on month input. Works great on web. Works great on mobile. Works for all locales eg 01/10/2014 - is that the 1st October or 10th Jan? I expect we'll be seeing this birthday picker format a lot more in future.

A datepicker is just a poor solution all round. So many clicks! In my opinion, a datepicker is only useful when knowing the day of the week is important eg booking tickets.

Update 2/6/2016: I am from UK, so I am more familiar with day/month/year formats, rather than month/day/year. However, users who will use their cursor to select the month, I believe it is much easier having the select box first, rather than going input > select box > input. The comment date is 2nd June, not 6th Feb ;)

For an advanced user text input is the best, if the user knows the date format, it is very fast. For a not so advanced user I suggest using a datepicker. Since usually you also have advanced and non-advanced users I suggest a combination of text input and datepicker.