I should start off by saying that this anime is great. It has involved characters, a solid plot, and wonderful art. But watching this show would be a horrible mistake. The manga surpasses it in every way, and watching Blade of the Immortal will do nothing but spoil the plot.
It's evident that a lot of time and effort was put into doing the manga justice. However, the nuances and subtleties which make Samura's work so great are simply not suited for anime. The mangaka himself was originally against animating Blade of the Immortal. I can't imagine why he changed his mind; it was clearly a mistake.
In many ways, this anime felt like a slideshow of the manga with music thrown in at the last minute. As can be expected when over 20 volumes are compressed into 13 episodes, the plotline was rushed, and character development was mostly left out. I'd write more about the high points of the anime (because there are plenty), but frankly, they can all be found in the original.
Though a lot of long-time BotI fans are insulted by this adaptation, personally, I enjoy it. I plan to watch it again before I get the next volume of the manga, as a quick recap of the story. It's nice as a summary, but in no way can it take the place of the original.