It depends what part of the world you are in. I'm in Sydney Australia, so our longest and second longest will be in December. Anyway, I found out from looking at the Sydney Observatory site that this year, the exact moment when the sun is at its furthest north in the southern hemisphere is 4.06am on the 22nd June. So this would be technically the moment of WINTER solstice for us, making the 22nd June our shortest day. The second shortest was probably the day before, the 21st. This was what was posted on that site on the 22nd June (it's the afternoon of the 23rd here now):

This year winter solstice, which is the time the Sun is at its furthest north for the year, occurs at 4:06 am Australian Eastern Standard Time on Friday 22 June 2007. That means that Friday is the shortest day. Since the solstice occurs during the night of 21/22 June that is the longest night.

As most of the world apart from New Zealand is behind Australian time, in the time zones of countries like the UK and the USA the solstice occurs the day before that in Australia. Hence there is confusion for some people who have calendars with information sourced from overseas and who consequently think that the solstice and the shortest day are today. I should also point out that though from Friday onwards the days will start to get longer, the differences initially from day to day are only a few seconds and hence not noticeable.

The UK is 9 hours behind us right now, so their moment of summer solstice would be 7.06pm on the 21st June, and Mudcat time is 14 hours behind us, so the moment of summer solstice in that timezone would be 2.06pm on the 21st. Both those times are before sunset so the 21st would be the longest day and either the 20th or the 22nd would be the second longest - might be a couple of seconds difference between one and the other, but since those times are later in the day, I'd guess it would be the 22nd.

Another interesting point they make on that site is this:

...please note that the earliest sunset for the year did not occur on the solstice, but about 10 days earlier. Similarly, the latest sunrise will not be on the day of the solstice, but about 10 days later.

If you are in the Northern Hemisphere, remember that they are talking about the WINTER solstice. I think in the summer, the earliest sunrise is about 10 days before the solstice and the latest sunset comes about 10 days after the solstice.