The first post to this question noted that liberals and conservatives have differing ideas on the role of government. This post specifically addresses their differences on social issues.
Liberals and conservatives have always disagreed on what government should do and how it should do it. In the past, a lot of this disagreement has been based on government spending and military policy. However, in recent years, we have seen an even greater schism between liberals and conservatives on social issues.
Socially, liberals generally advocate for a more inclusive, tolerant society. Issues such as gay marriage, abortion, universal healthcare, and immigration have been keystones of Democratic party platforms and proposals.
Conservatives, on the other hand, usually prefer to maintain the status quo. We see this with their attempts to define marriage as a union of a man and a woman, or their opposition to Obamacare legislation. Sometimes they go beyond maintaining the status quo and propose reverting back to a previous condition, as when they consider repealing Obamacare. We have also recently seen a fracturing of conservative ideology along religious lines, with parties such as the Tea Party and the Constitution Party seeking to frame their political views within a religious context. You might consider these parties to the be the more "radical" conservative wing.
The social aspects of political ideology have become more divisive than ever before. How these divisions are addressed by the existing political parties will have a lot to do with how political power is won and exercised in the future.