Really the main remnants of Prussian culture to stick around to the current day are Germany's expansive social welfare system and his focus on education. The identity was systematically destroyed after World War 1 more than 2. Germany had four (or five) cultural identities in the 20th century: Prussian, Weimar, Nazi, and Postwar/modern.

The culture of Germany underwent an incredible shift after each world war, and the main forces behind the shift were the victorious allies. With the removal of the Prussian crown, a parliamentary system was formed (to very limited popularity--facing a worker's revolution almost immediately), but lasted shortly, as the Weimar Republic was established at the end of WWI

The Weimar era was a period of increased liberalism and free thought amongst Germans. At this time the Frankfurt school had its beginnings, and more Jews (although legally equal according Article III of the Imperial Constitution [Verfassung des Deutschen Reiches] , they were very much second class citizens) found their way into intellectual circles. Their influence on German advancement of the time cannot be overlooked--five of the nine Weimar winners of the Nobel prize in sciences were of Jewish descent. Weimar Germany saw advancement of German literature, cinema, science, design, most arts and sciences. Germans experimented--often publicly--with homosexuality, drug use, jazz, and avant garde art: jazz music, expressionist film and literature like Hesse and Remarque.

Some reactionaries, disgusted at the liberal attitudes of the Weimar Republic, supported the NSDAP rise to power, hoping to use them as a pawn to inspire a conservative base in Germany and return to the monarchy. That didn't work out well for them, and the Nazis secured a power base enough to take control and nazi Germany is really mostly wartime (or preparing for wartime), and I won't be describing that in a response about post-war cultures.

Postwar Germany then was a fractured and defeated place, compared to the prideful Prussian past. The allies ran extensive denazification, going as far as running background checks to weed out past supporters, party members, and even soldiers for deeper evaluation (and usual arrest) before issuing ration cards.

From this period of a destroyed (I mean truly destroyed, most of the industrial cities in Germany were pounded into rubble) left for the largest postwar creative style--Trümmerliteratur and Trümmerfilm, literally rubble literature and rubble films, showing the destroyed both literally (here's a slideshow of cities pre-war and here's one of the aftermath) and ideologically, being released two, three, up to five (officially, rumored much much longer) years later to see a destroyed Germany with a different cultural mindset.

With foreign aid to entrepreneurs, and a near blank slate for businesses (as all the established ones have been reduced to shells), new equipment was available and accessible to German industrialists, and the onus of work for both German men and women (women were the main force for reconstruction of cities and early industry, as there were simply too few men due to the war and previous nazi ties), leading to the cultural stereotypes that are held today.

EDIT: If you're looking for a book that goes deeper into prussia than "Prussia was not catholic. Prussia had a pretty cool army. Prussia united Germany." I highly suggest Iron Kingdom: The Rise and Downfall of Prussia, 1600-1947 by Christopher Clark.

The military of East Germany, the Nationale Volksarmee (National People's Army) internally retained much of the Prussian military tradition, as opposed to the West German Bundeswehr which abandoned most prior German military tradition as a result of the Second World War. This was manifested in the uniforms and training of the NVA soldiers, and certain ceremonies like the guarding of the Neue Wache in Berlin by the Wachregiment „Friedrich Engels“, and the Großer Zapfenstreich, or Grand Tattoo, a yearly torchlight review of the NVA. Other traditions existed in the awards and decorations of the NVA and the music, with marches like the Yorckscher regularly used for parades.

I'm not aware if this happens in other militaries worldwide, but Prussian traditions and culture are also kept in the Chilean army (which was reformed from a french-inspired force into a prussian one at the beginning of the 20th century; the army was deemed to need some modernization after the Pacific War, and the franco-prussian war inspired the government to seek German advisors). It's not so easy finding good quality videos, but here's something I found on youtube, a recording from the 2011's great parade where you can see the influence.

http://www.youtube.com/watch?v=x2cejI6-kHE

Interestingly, these "World War 2 era" uniforms were replaced by older Prussian ones for the parade this last year. http://www.youtube.com/watch?v=yq3xO0OYykg

Please excuse any grammar mistakes, english is not my first language. Hope this answer is somewhat satisfactory!

Prussia introduced special type of employee for the administration in all government departments. Those employees (Beamter) couldn't be fired and the retirement conditions were good. Even postal services had this type of an employee. The background for this is the assumption of a better loyalty. They exists today.

Prussia forced the use of nowadays German and oppressed dialects and languages like Low German (Plattdeutsch), which was a common language in northern Germany until 18th century. So nowadays German today is a result of Martin Luthers Bible translation and Prussian force.

Prussia introduced a collection of laws called Bürgerliches Gesetzbuch (Civil Code) which is based on a french template. Instead of having thousands of different laws, this collection regulates private law.

The Civil Code is divided into five books (Wikipedia):

* General part - it contains important basic rules for the second to fifth book (see clip art )
* Law of Obligations - Roman law influenced the law of obligations contains provisions for mandatory contracts such as purchase agreements, leases or service contracts
* Property law - the German law embossed property law includes, in particular arrangements for ownership and possession
* Family law - the German law influenced family law now contains the essential rules on marriage and family
* Inheritance - the German law of succession embossed contains comprehensive provisions to Testament , succession and heirs 

I'd like to add East German architecture from 1950 - 1960 (ish).

The BRD adopted a decentralized planning system. Apart from some federal laws and guidelines, the Bundesländer as well as individual citites enjoyed a considerable independence to adminitrate the reconstruction process. Some citites chose to reconstruct the old historical city centers (i.e. Freiburg) while others didn't. Nevertheless, the federal government in Bonn never tried to establish a nation wide architectural trend.

This happened in the DDR. East German planners soon found themselves under strict surveillance from centralized administrations in Berlin, and architects had to consider "die 16 Grundsätze des Städtebaus" (1950), or "The 16 Principles of Urban Planning". A lot of people nowadays associate East German cities with dull and greyish concrete landscapes. I'm not going to say that it isn't true, beause it often is, but there are exceptions. Eisenhüttenstadt, formerly Stalinstadt, in Brandenburg is a good example. The first years of the republic were heavily influenced by Stalinist ideals. This was also true for planning and architecture. Stalin's fascination for pompous and majestic architecture can easily be seen in Moscow, where "wedding cake" (ger: Zuckerbäckeri) influenced buildings are common. And as well know, if Stalin fancied something, then it was made into an offical state policy.

In 1950, during the third Socialist Party congress in Berlin, President Walter Ulbricht, a devout stalinist, made it very clear that architecture in DDR should follow established German traditions - "Die Nationale Traditon". This did not mean that architects were to celebrate pre war-authorities, nor were they to reconstruct city centers to pre war-standards. The main focus of die nationale Tradition was to incorporate good and homage-able German traditions into the new socialist German state. As a result, many houses constructed between 1950 and 1960-ish bears a distinguishable Prussian, neoclassical touch. This era did however not last very long. Chrustjov deemed the wedding cake-style as expensive and ineffective and definitely uncapable of solving the urgent housing question. In short: a very unsocialist fashion. Soon after that, die Nationale Tradition was phased out as well.

Sources: Hall, Peter, 2002: "Citites of Tomorrow - an Intellectual History of Urban Planning and Design in the 20th Century", Wiley & Blackwell. Kirchner, Jörg, 2010: "Architektur nationaler Tradition in der frühen DDR (1950-1955). Zwischen ideologischen Vorgaben und künstlerischer Eigenständigkeit". Universität Hamburg. Bundeszentrale für politische Bildung, 2005: "Die 16 Grundsätze des Städtebaus" [http://www.bpb.de/gesellschaft/staedte/wiederaufbau-der-staedte/64346/die-16-grundsaetze-des-staedtebaus]