Calculating Resistance (Nerd Sniping)
Python, 329 chars

import sys
N=[[1]]+[map(int,x.split())for x in sys.stdin]
N[-1][0]=1
n=len(N)
S=[set([i])for i in range(2*n)]
for x in range(n):
 C=S[2*x]
 for y in N[x][1:]:C|=S[2*y+1]
 for x in C:S[x]|=C
V=[0]*(2*n-1)+[1]
for k in range(999):
 for i in range(1,2*n-1):V[i]+=sum((V[j^1]-V[i])/N[j/2][0]for j in S[i])/9./len(S[i])
print 1/V[1]-2


Calculates the resistance by doing a voltage relaxation on the circuit.  First it tacks on a 1 ohm resistor to the start and changes the last resistor from 0 ohm to 1 ohm.  Then it sets the input voltage to 0 and the output voltage to 1 volt.  After simulating current flow through the network, the network resistance is calculated using the voltage drop across the first 1 ohm resistor.

Each resistor is given two numbers, the number for its left terminal and the number for its right terminal.  Resistor r's left terminal is 2*r and its right terminal is 2*r+1.  The input is used to calculate S, the sets of terminals that are connected together.  Each terminal is given a voltage V[t] and a relaxation is done by raising the voltage if current is net flowing into a terminal set and lowering the voltage if current is net flowing out.