Famously many members of the 1970's/80's West German domestic left-wing terrorist organization 'Rote Armee Fraktion' (RAF) at one point or another were all hiding out in east Germany either with implicit knowledge or on active invitation of the East-German intelligence.

There have been a couple of cases of people voluntary coming to live in the DDR. Some were political, some personal some even professional. Most famously there was the case of Berthold Brecht, the playwright. After being kicked out of Germany by the Nazis and spending WWII in Hollywood, he returned to his old theater in Berlin and after said theater found itself on the East side of the city, extensively toured all of Germany, east and west, an probably could have settles anywhere, but chose not only to stay in east Berlin but effectively embraced the DDR communist party line and made increasingly communist-tinted plays. Truth be told, he always had a leftist streak and did not suffer opportunists likely. That's why he ran foul of the Nazis in the first place.

However no one ever climbed over the Berlin Wall. Most commonly defectors entered legally on a visitors or transit visa and once in East Germany presented themselves to the Stasi. It's just easier that way.

Modified from an earlier answer of mine

The migration from East to West, Republikflucht, was massive and an enormous problem for the GDR. But the huge size of this outflow does obscure the fact that more than a few people from the Western zone/FRG did opt for life within the peasant and workers' state.

Some of this West-East migration was explicitly political in nature and very high-profile. This list is far from comprehensive, but gives a general idea that some famous defections did occur. Most of the defections by Germans from the FRG to the GDR were connected to Stasi intelligence. The Stasi recruited spies within the FRG and it became quite common for them to defect if it became clear they were about to be caught. But the nature of cloak and dagger work makes these cases quite confusing still. Some of these defectors may have been operating out of ideological convictions, but others were semi-coerced by the fact that they had been compromised by the Stasi. For example, Hans Joachim-Tiedge was one of the famous cases from the 1980s and his rationale for defecting is still quite nebulous.

But there were other cases of defection that had little to do with espionage. Manfred von Brauchitsch defected to the GDR to escape his tax debts and the GDR offered him financial incentives to do so. Even more enigmatic is the case of Otto John who defected to the GDR in 1954 partly out of the conviction that West German rearmament and the continued presence of Nazis within West German society ran counter to the ideal that German after 1945 had turned its back on National Socialism.

John's case highlights an important point about the Cold War in Germany, especially in its early decades. Although it is tempting to conceptualize the two Germanies as "democracy vs. totalitarianism," the distinction was less clear cut during the time. Although Adenauer's West Germany made public commitments to democracy, it possessed a high degree of social conservatism and one of the pillars of its political society was a fervent anticommunism. For many Germans that rejected Nazism, the latter was particularly troubling given that the FRG adapted a very lenient stance towards denazification. Adenauer cemented a silent compact that offered former Nazis (at least those who were not directly responsible for major crimes) a place in the new government provided that they kept their mouth shut about the previous regime and did not directly undermine democratic institutions. This was something that fed a great deal of ideological dissatisfaction among a number of West Germans. Although things like the 1953 East Berlin uprising and the Berlin Wall soiled the image of the GDR and communism, a reaction against the social and political strictures of the Adenauer state was a consistent theme within the FRG throughout the Cold War. This discontent with the FRG's stuffy political system fed into some of the West-East migration.

There were other examples of migration on the basis of ideological affinities or a rejection of American cultural hegemony. Wolf Biermann left Hamburg for the GDR because he felt that the GDR stood for, as he put it in a recent interview, "the better Germany." Nor should this cultural or ideological appeal of a socialist Germany be entirely discounted; Victor Klemperer, whose diaries are an especially perceptive window into the Third Reich, elected to stay in the GDR on account of his dislike of the FRG's Christian conservatism and the crass materialism of its American patron. Klemperer's diaries from the postwar period show little love for the SED's dictatorship, but he saw it as the "lesser evil." Other West-East migrants moved because of the capitalist competition within the FRG did not sit well with their ideal of a renewed postwar Germany.

The SED naturally trumpeted any West-East migration as a sign that it held the moral high ground in German division. GDR state media asserted that Republikflucht was a Western intelligence plot to undermine the GDR while maintaining that migration in the other direction was a sign that good Germans had recognized the moral superiority of a reformed Germany under the SED's auspices. But there was always a difference between rhetoric and reality and the SED never quite trusted its defectors. The Stasi often kept very close tabs on them and there was a fear that a double-defection could embarrass the GDR.

There were other, much less high-profile West-East migrations. One facet of German division was that it did divide families and some emigration did occur to take care of an elderly parent or other relation. Such family-based emigration was typically East to West, especially since the GDR government did not want to pay for pensioners in an already burdened planned economy. Other West-East migrants were former GDR citizens who found that life in the West was less romantic than the image of the Wirtschaftswunder presented. There was also a jump in West-East migration when the FRG introduced conscription for the newly formed Bundeswehr. Although Bonn's conscription did have provisions for conscientious objectors, these provisions were not as lax as they would be in later years. Most of these provisions were limited in the early decades of the FRG to religious convictions, which limited the options for those Germans that did not want to serve for non-religious reasons. By the same token, one of the push factors for West-East flight in the mid-1950s was also fear that the NVA would enact its own form of conscription, showing that the war-inspired ohne mich (without me) sentiment transected the Iron Curtain in Germany.

But West to East migration levels were always much lower even when there were similar factors at play such as conscription. In the case of conscription, West Berlin whose Free University and exemption from conscription acted as a sump for ohne mich types. The FRG system also proved much more willing to adapt to circumstances such as the adaption of Zivildienst (alternative civil service) in 1973 for objectors to conscription in the Bundeswehr. The FRG was not only a more economically successful Germany, Bonn also possessed a degree of popular legitimacy the GDR lacked. But such emigration to the GDR did occur, even if at a much lower rate than Republikflucht in the other direction.

Sources

Frei, Norbert. Adenauer's Germany and the Nazi Past: The Politics of Amnesty and Integration. New York: Columbia University Press, 2002.

Kundnani, Hans. Utopia or Auschwitz?: Germany's 1968 Generation and the Holocaust. New York: Columbia University Press, 2009.

Major, Patrick. Behind the Berlin Wall: East Germany and the Frontiers of Power. Oxford [u.a.]: Oxford University Press, 2011.