Edit: As of Inkscape 0.91, markers take the color of the object. Extensions and workarounds are no longer needed.
This is one of the most frequently asked questions about Inkscape, so I'll just quote from their site:
How do I change the color of markers (e.g. arrow ends)?
By default, markers are black. You can change their color to match the color of the stroke of the object they are applied to by enabling an effect: Extensions > Modify Path > Color Markers to Match Stroke.
However, this script is an external Python tool, so you might be out of luck if you use Inkscape on Windows or Mac OS X (which has Python, but is missing some dependency). In that case, there is no other way than to edit the SVG source for the objects. Painful!
This should change at some point in the future, as it is one of the most requested features (see this bug report which gathers progress, or lack thereof). Citing one of the developers (in 2008):
There's no doubt that this should be the default behaviour, and it's one of the most requested features (bug 165865). But it's a question of someone taking the time to implement it.
and a testimonial from a user, in 2012:
The original bug was reported in 2004... after 8 years I start to believe I can only make black arrows