We obtained over 90 hr of spectroscopic observations of four exoplanetary systems with the Hobby-Eberly Telescope. Observations were taken in transit and out of transit, and we analyzed the differenced spectra--i.e., the transmission spectra--to inspect it for absorption at the wavelengths of the neutral sodium (Na I) doublet at Delta *l Delta *l5889, 5895 and neutral potassium (K I) at Delta *l7698. We used the transmission spectrum at Ca I Delta *l6122--which shows strong stellar absorption but is not an alkali metal resonance line that we expect to show significant absorption in these atmospheres--as a control line to examine our measurements for systematic errors. We use an empirical Monte Carlo method to quantify these systematic errors. In a reanalysis of the same data set using a reduction and analysis pipeline that was derived independently, we confirm the previously seen Na I absorption in HD 189733b at a level of (-- 5.26 ? 1.69) X 10--4 (the average value over a 12 A integration band to be consistent with previous authors). Additionally, we tentatively confirm the Na I absorption seen in HD 209458b (independently by multiple authors) at a level of (-- 2.63 ? 0.81) X 10--4, though the interpretation is less clear. Furthermore, we find Na I absorption of (-- 3.16 ? 2.06) X 10--4 at <3 Delta *s in HD 149026b; features apparent in the transmission spectrum are consistent with real absorption and indicate this may be a good target for future observations to confirm. No other results (Na I in HD 147506b and Ca I and K I in all four targets) are significant to >=3 Delta *s, although we observe some features that we argue are primarily artifacts.