Substitute oregano or basil if you're making a tomato-based recipe. It's a different and stronger flavor, but would work well for meatballs, meatloaf, pasta dishes and more.
Use tarragon instead of thyme on chicken and fish dishes.
Add rosemary to the recipe if your lamb or pork recipe calls for thyme and you're all out. Rosemary and oregano also work well with potato recipes.
Know that marjoram and parsley are other common substitutes for thyme. Parsley won't add much flavor but will give your dish some color.
Grab Italian Seasoning if you have that in your spice rack. It actually contains thyme, so it should work in your recipe.
Leave out thyme if you don't have it. Many cooks suggest that you don't even try to substitute for thyme--just skip it.