The thermal conductivity $K$ and the thermoelectric power $Q$ of single-crystal samples of rutile were measured from 2 to 300\ifmmode^\circ\else\textdegree\fi{}K. Pure, niobium-doped, vacuum-reduced, and hydrogen-reduced specimens were investigated. The thermal conductivity of the pure crystals is similar to that usually found for insulators, with a maximum at about 15\ifmmode^\circ\else\textdegree\fi{}K. Boundary scattering determines $K$ below the maximum, and in the range 25 to 100\ifmmode^\circ\else\textdegree\fi{}K the conductivity varies exponentially with temperature, which is characteristic of umklapp scattering. The Callaway expression for $K$ was used to fit the data over the entire temperature range. From measurements in both the $c$ and an $a$ direction, it was found that the anisotropy ratio $\frac{{K}_{c}}{{K}_{a}}=1.5\ifmmode\pm\else\textpm\fi{}0.1$ above 25\ifmmode^\circ\else\textdegree\fi{}K. The ratio decreases below 25\ifmmode^\circ\else\textdegree\fi{}K to a limiting value of 1.05\ifmmode\pm\else\textpm\fi{}0.1. A sample doped with 0.1% Nb has a thermal conductivity quite similar to the pure Ti${\mathrm{O}}_{2}$. The $K$ of the reduced samples is quite depressed at low temperatures and a discussion of possible processes is included. On oxidation of a reduced sample it was discovered that the thermal conductivity did not recover completely to the original values measured on the same specimen before reduction. For one crystal a comparison of $K$ in the reduced and reoxidized states yields values for the extra thermal resistance which are compatible with the number of point defects introduced by the reduction. The thermoelectric power of the semiconducting samples (Nb-doped and reduced) increases rapidly below 100\ifmmode^\circ\else\textdegree\fi{}K, indicating a large phonon-drag contribution.