The following items upgrade Smite by granting additional effects:
Skirmisher's Sabre: Challenging Smite can be cast on enemy champions, revealing them for 4 seconds, reducing their damage against you by 20% and making them take 60 - 162 (based on level)true damage over 3 seconds from your basic attacks for the duration.
Casting Smite on large monsters instantly harvest a bonus that is available once per spawn, regardless of who killed the monster. Colored bubbles come out of the monster if the bonus is available, and this is only visible if you have Smite. The exceptions are the Rift Scuttler, and the Rift Herald which doesn't give any bonuses (Dragon and Baron Nashor are epic monsters).
Blue Sentinel: restore a large amount of mana over 2 seconds (25% of your maximum mana).
Red Brambleback: restore a large amount of health instantly (20% of your maximum health).
Ancient Krug: for 90 seconds every 6th basic attack stuns minions and monsters. Additionally, you can attack a tower to expend the buff early - dealing a large amount of bonus true damage 65 - 330 (based on level).
Crimson Raptor: grant you true sight for a short duration the next time you are spotted by an enemy ward for 90 seconds.
Greater Murk Wolf: summon a rift spirit that grants sight over the nearby crossroads for 90 seconds. Whenever an enemy champion comes in range of the nature spirit, it will chase them for a short duration.
Gromp: for 90 seconds, poisons enemies who attack you, dealing 10 + (5% bonus health) magic damage over 3 seconds.
Smite is generally used for jungling. Beyond dramatically speeding up clear time, its high damage provides a strategic last-hit advantage at high-priority buffs like Dragon and Baron Nashor.
Smite can also be used to push a lane more quickly. When doing so, it's generally best to save Smite for cannon minions.
An unconventional use of Smite is to instantly and unexpectedly kill a minion to land skillshots such as Rocket Grab or Death Sentence on enemy champions behind it.
Smite deals true damage, so it will always deal the stated amount; it cannot be reduced or amplified in any way other than a few exceptions, such as the bonus damage against the Rift Scuttler under hard crowd control.