As Vampiric Scepter is a necessary component for almost all of the life steal items, it is useful for any stage of the game.
Vampiric Scepter increases the sustain of any champion, but it is best used with basic attacking champions as life steal only works with basic attacks. Ranged champions, such as Ashe or Tristana, are able to restore health while being relatively safe. Melee champions, such as Jax or Wukong, are in more danger to be damaged if an enemy champion is nearby.
Vampiric Scepter is often used with Doran's Blade, allowing champions to stay in lanes for extended periods of time without needing to go back to base to heal. Doran's Blade is often the preferred item as it also adds health, but its drawbacks are not building into other items.
If you're having trouble sustaining in top or mid as AD, do not rush Vampiric Scepter - at 900 gold and only 10% lifesteal, given low (sub 150) total AD values, you usually won't be able to sustain enough from trading and lane minions. Note that 900 gold is 18 Health Potions - or 2700 total health from regen. Consider either Doran's Blades or Health Potions.