What cocktails can I make with just a bottle of vodka?

Moscow Mule (with lime and ginger beer), Vodka Martini (with dry vermouth), Bloody Mary (with tomato juice and seasonings), and Vodka Sour or Lemon Drop (with citrus and sugar). Vodka is flavorless on purpose so it works with almost any mixer.

Vodka's neutrality is its strength — it adds ABV without adding flavor, so the other ingredients dominate. With just a bottle of vodka and pantry items: (1) Moscow Mule — vodka, fresh lime juice, ginger beer over ice in a copper mug or highball. (2) Vodka Martini — 2.5 oz vodka, 0.5 oz dry vermouth, stirred, lemon twist or olive. (3) Bloody Mary — vodka, tomato juice, Worcestershire, hot sauce, salt, pepper, celery; the recipe is more about ratios of seasoning than precise measures. (4) Vodka Sour — vodka, fresh lemon juice, simple syrup, optional egg white. (5) Lemon Drop — vodka, fresh lemon, Cointreau (if available), sugar rim. (6) Vodka Tonic — vodka, tonic water, lime wedge, highball over ice. Add Cointreau and the range opens up further: Kamikaze (equal parts vodka, Cointreau, lime), Cosmopolitan (with cranberry), Vodka Gimlet. Add fresh espresso and you have the Espresso Martini (with coffee liqueur ideally). Vodka pairs cleanly with everything from citrus to dairy to coffee; the limitation isn't the spirit, it's the modifier inventory.