Is there a Baire Category Theorem for Complete Topological Vector Spaces?

The Baire theorem also holds for topologically complete spaces, i.e. Tychonov spaces that are a $G_\delta$ in some compactification;

IIRC this includes topological vector spaces that are complete in their uniformity as well. [edit] This is actually false, see the answers for this question....

For large classes of TVS (like Fréchet spaces or Banach spaces) we can apply the metric version, and many weak topologies are (sequentially) complete as well.

More on completeness of TVS can be found here

According to Birkhoff-Kakutani theorem, a topological vector space is metrisable if and only if it is Hausdorff and $0$ has a countable neighborhood basis. (For a topological vector space, being Hausdorff is equivalent to $\{0\}$ being closed.)

Therefore, a complete topological vector space in which $\{0\}$ is closed and $0$ has a countable neighborhood basis satisfies the Baire category theorem.