A Servant that has been summoned and then returned to the Throne of Heroes will not remember their first summoning during any subsequent summonings. Under normal circumstances, each time a Servant is summoned, it is actually a copy of the Servant derived from the Throne of Heroes that manifests into the world, and changes to that copy do not affect the version of the Hero stored in the Throne of Heroes. (Servants have copy semantics, so to speak.)
However, in Fate/stay night and Fate/Zero, Saber and Gilgamesh do not follow this general rule.
- Gilgamesh remained in the world from the start of the 4th Grail War until at least part way through the 5th Grail War, and hence has memories of this entire time period (but he would not have memories of other summonings).
- Saber, having not yet died at the time of her summoning to the 4th and 5th Grail Wars, was not copied from the Throne of Heroes in the first place. She retains continuity of memory between the two wars. (Saber has move semantics, if you will.)