If the grout looks icky, the tile (and the whole bath) looks icky too. Sometimes grout can get discolored and no amount of cleaning and scrubbing seems to improve things.
A friend of ours was constantly battling the grout in her old condo and used one of these whitening pens (2 pack, $12.95) and was very happy with the results.
It's called Grout-Aide and is anti-bacterial and anti-mold, non-toxic and odorless. It is water-based and fast drying to a waterproof finish/seal. Each marker covers 175 lineal feet of grout.
Definitely not the most glamorous product ever, but from what we've seen and heard, it works!
Available at Solutions.