How would the world be like right now if we didn't have Abraham Lincoln?

It is never possible to know for certain how history would have been different in the absence of a single individual. If there had not been an Abraham Lincoln, it may be that the Civil War would have turned out differently, and the Confederacy would have been successful in seceding from the Union, and who knows, perhaps it would continue to practice racially based slavery, even in the year 2010. But we don't know that. It is also possible that some other President would have succeeded in defending the Union and in freeing the slaves. Many things are possible.