In order to get a better quality answer to this, you should specify what you mean by “this generation.” Depending on how you define that, the answer could be different.
One of the most important events in recent history was, of course, the terrorist attacks of September 11, 2001. If we define “this generation” as people who are anywhere from, say, 23 to 30 years old today, this event would likely be the most important in their political socialization. These people would have been anywhere from 12 to 19 at the time of the attacks. The attacks would have done a great deal to socialize these people with regard to what their attitudes towards foreign policy are and what sorts of issues they think are important.
If you go a little bit farther back, the Clinton impeachment might be a major source of political socialization. This happened in late 1998 and 1999, though the scandal that led to the impeachment had been in the news for some time before late 1998. The scandal and the behavior of both parties during the scandal might have socialized people to distrust and disrespect the political parties.
Other generations, of course, will have very different important events in their socialization. These are two of the most important events for the generation that is old enough to be politically active but is still relatively young today.