Find the curve defined by the equation
\[r = \cos \theta + \sin \theta.\](A) Line
(B) Circle
(C) Parabola
(D) Ellipse
(E) Hyperbola

Enter the letter of the correct option.
We are given that $r = \cos \theta + \sin \theta.$  Then
\[r^2 = r \cos \theta + r \sin \theta,\]so $x^2 + y^2 = x + y.$  We can write this equation as
\[\left( x - \frac{1}{2} \right)^2 + \left( y - \frac{1}{2} \right)^2 = \frac{1}{2}.\]Thus, the graph is a circle.  The answer is $\boxed{\text{(B)}}.$

[asy]
unitsize(2 cm);

pair moo (real t) {
  real r = cos(t) + sin(t);
  return (r*cos(t), r*sin(t));
}

path foo = moo(0);
real t;

for (t = 0; t <= pi + 0.1; t = t + 0.1) {
  foo = foo--moo(t);
}

draw(foo,red);

draw((-0.5,0)--(1.5,0));
draw((0,-0.5)--(0,1.5));
label("$r = \cos \theta + \sin \theta$", (2,1), red);
[/asy]