The default Matlab default line spec and colormaps are astoundingly crude. This function creates distinguishable colors by spacing them out ~equally in *perceptive* space, not in RGB space. It is based off the research of professor Cynthia Brewer (colorbrewer!) but amazingly easy to use.
This function creates an Nx3 array of N [R B G] colors
These can be used to plot lots of lines with distinguishable and nice looking colors.
lineStyles = linspecer(N); makes N colors for you to use: lineStyles(ii,:)
colormap(linspecer); set your colormap to have easily distinguishable colors and a pleasing aesthetic
lineStyles = linspecer(N,'qualitative'); forces the colors to all be distinguishable (up to 12)
lineStyles = linspecer(N,'sequential'); forces the colors to vary along a spectrum

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Examples demonstrating the colors.

% LINE COLORS
N=6;
X = linspace(0,pi*3,1000);
Y = bsxfun(@(x,n)sin(x+2*n*pi/N), X.', 1:N);
C = linspecer(N);
axes('NextPlot','replacechildren', 'ColorOrder',C);
plot(X,Y,'linewidth',5)
ylim([-1.1 1.1]);

% SIMPLER LINE COLOR EXAMPLE
N = 6; X = linspace(0,pi*3,1000);
C = linspecer(N)
hold off;
for ii=1:N
Y = sin(X+2*ii*pi/N);
plot(X,Y,'color',C(ii,:),'linewidth',3);
hold on;
end

% COLORMAP EXAMPLE
A = rand(15);
figure; imagesc(A); % default colormap
figure; imagesc(A); colormap(linspecer); % linspecer colormap

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Credits and where the function came from:

The colors are largely taken from:
http://colorbrewer2.org and Cynthia Brewer, Mark Harrower and The Pennsylvania State University
She studied this from a phsychometric perspective and crafted the colors
beautifully.

I made choices from the many there to decide the nicest once for plotting lines in Matlab. I also made a small change to one of the colors I thought was a bit too bright. In addition some interpolation is going on for the sequential line styles. An Apache-Style Software License is included in the file.