Settlers of Catan - Longest Road!
Python 2, 445 400 bytes
I'm a fan of Settlers, so this challenge was fun.
T=&quot;^&quot;
Z=26
A=T*52
for i in range(11):A+=(T*(i%2)*3).join(x for x in raw_input()).center(Z,T)
A+=T*52
def f(c,p=0,l=0,B=A):
 b=l;C=B[0:p]+T+B[p+1:];n=(Z,1)[p%2]
 for i in(p&lt;1)*range(390):
    if(i/Z%2&lt;1&amp;i%2&gt;0)|(i/Z%2&gt;0&amp;i%2&lt;1):b=max(b,f(c,i))
 for i in(p-n,p+n)*(B[p]==c):
    for j in(i-Z,i-1,i+1,i+Z)*(B[i]in c+&quot;_&quot;):b=max(b,f(c,j,l+1,C))
 return b
i=l=0
for x in A:
 if x&lt;T:i=f(x)
 if i&gt;l:c=x;l=i
print c,l

Score reflects replacing each occurrence of 4 spaces with a tab.
Explanation
The lines before the function definition read the input, and build a normalized board into a single string variable.  The process inserts &quot;^&quot; characters into the short lines representing the vertical road segments.  It also pads the board with &quot;^&quot; characters.
^^^^^^^^^^^^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^^^^^^^^^^^^
^^^^^^________RR_R_^^^^^^^
^^^^^^_^^^_^^^R^^^_^^^^^^^
^^^^__RR_R_RRR_____R_^^^^^
^^^^B^^^_^^^_^^^_^^^R^^^^^
^^_B_________B__OO_OOR_^^^
^^B^^^_^^^_^^^B^^^_^^^R^^^
^^BB_BBB_____B____RR_R_^^^
^^^^O^^^B^^^B^^^_^^^O^^^^^
^^^^OO__BB_BB__OOO_OO^^^^^
^^^^^^O^^^_^^^O^^^_^^^^^^^
^^^^^^_O_OOO_O_____^^^^^^^
^^^^^^^^^^^^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^^^^^^^^^^^^

When called with the default parameters, the function returns the length of a road of a given color.  The first loop is active only when the position (p) parameter was supplied.  It recursively finds the length of the road at each valid road position, and keeps track of the longest one.  When there is a road at the position parameter, the function recursively adds the length of adjacent roads of the same color.  The road is replaced with a &quot;~&quot; in the working copy of the board to ensure it doesn't recount segments that have already been counted.
The code following the function definition calls the function for each color in the board, and prints the highest scoring color and length.
Demo it here