= Regular functions on the punctured affine plane
For $W=\mathbb A_k^2\setminus\{0\}$, restriction to $D(x)$ and $D(y)$ gives
$$
\Gamma(W,\mathcal O_W)=k[x,y]_x\cap k[x,y]_y=k[x,y].
$$
The intersection is taken in $k(x,y)$ and the equality follows from <unique factorization>: a reduced denominator dividing powers of both $x$ and $y$ is a unit. The inclusion $W\hookrightarrow\mathbb A^2$ induces an isomorphism on global functions but is not an isomorphism, so $W$ is not an <affine variety>.
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