Is the graceful labeling conjecture still unsolved?

It's still open. At least if we are to believe this recent (2011) Stanford Thesis, which gives an extensive survey of the problem.

The problem is one of those 'disease' problems to which lots of people come up with bad proofs for. It does however appear to be solved for certain cases of trees.

You can also find and trace news about best-known kinds of graph labeling, in a dynamic survey by J. A. Gallian. According to it's last version, the conjecture is still unproved.