These seem to be fairly common with the airports and trains in European countries. Everything shuts down for a day, usually announced in advance, inconveniencing travelers and such. Another one is currently in the news in Greece (due to the pending Olympics).
In the US, strikes are a last resort in negotiations, and generally last until the situation is resolved, however long that takes. Why do they only have one-day strikes in Europe?
Us Europeans haven’t got the dedication to keep up a longer strike 
Seriously, if I may give a WAG from a Dutch point of view. Strikes are more often used as an instrument in negotiations to show the employer that the employees are serious about their disagreement. A prolonged strike is in no-ones interest, not in the employer’s, nor in the employees’ (who have to fund the strike themselves).
For industries with clear effects on the public (such as transport) there is also the public opinion to take into account. Recent strikes of the railways have met strong public disapproval, even while the public did sympathize with the cause.
Therefore most strikes are organised in a ‘public-friendly’ manner. Employers do take a strike serious, even if it’s only for a day. It would be a waste of resources to have a longer strike. For The Netherlands there is a further reason, in that labour unions and employers habitually discuss lots of issues over extended periods of time (the ‘overlegeconomie’, economics of discussion), so both parties prefer to keep their relation good. Possibly the negotiations style in other countries is more confrontational.
A few years ago I was in Italy doing the factory acceptance tests of some telecoms equipment that our company were buying. The workers in the factory went on a half day strike . The reason ? it was in protest about self-employed workers paying a lower proportion of taxes compared to the non self-employed , because of under reporting of earnings.
Transport workers here have had two-hour strikes from time to time. They usually just call them “work stoppages” though.
In Germany short strikes (Warnstreiks) are used to demonstrate, at a particular point in renegotiatons of the contracts, that the union will be able to call a strike in earnest if necessary, and the strike will be effective. That is not automatically a given as union shops are disallowed (neither union membership nor union nonmembership may be a condition of employment), so employers might be tempted to rely on a call to a strike not being followed. Also, these last years, targeted warning strikes at selected plants allow unions to demonstrate that they are well informed about the choke points in the supply chain. All in all this flexing of muscles (sometimes also including short-time lockouts) allows the negotiating parties a good assessment of each other’s readiness to fight, which makes all-out, long-time strikes thankfully rare.
They are either measured action or temper tantrums. If the strikers are using it as a first step but are truly willing to go the distance if the short strike doesn’t work, then it’s a measured action. Why swat a fly with a nuclear bomb? If the strikers aren’t willing to go to the mattress when their short strike has no effect, then it’s just a temper tantrum.
At least in Britain, where the tactic is largely restricted to the Tube and the trains these days, it seems to be mainly about media leverage on public opinion. The population generally regards such services as underfunded and so has some sympathy with the unions, but dislikes disruption that is directly targeted at them. As a result, the reaction is a classic call of “something must be done”. This puts pressure on the operators (who are ultimately answerable to the government) to settle with the unions.
A couple of one-day strikes are usually enough for some sort of deal to be negotiated.