Wet Cooked Ham Slices
Extra water in cooked ham is 100% fine to eat, see here. In general, you can use the printed "use by" date if you're in the US and you'll be safe. I'm adding my answer to provide an authoritative source for you, so you'll know for certain you won't get sick from it.

Quotation, for @adamlynch:


  HAM:  In order to be labeled as "Ham," the product must be at least
  20.5% protein in lean portion as described in 9 CFR 319.104. Added water is permitted in a product labeled as "Ham." In fact, water
  will be declared in order of predominance in the ingredients
  statement. This is how the cure solution is introduced into a ham. 
  
  HAM AND WATER PRODUCTS X% of Weight is Added Ingredients: Product
  contains more additives than a "Ham Water Added," but the product name
  must indicate percent of "added ingredients." For example, "Ham and
  Water Product 25% of Weight is Added Ingredients" for any canned ham
  with less than 17.0% protein.


As you can see, water added to ham is perfectly safe to eat, as it's normal for it to be present in the ham.