The verb smite, meaning to inflict a heavy blow, is traditionally inflected smote (in the past tense) and smitten (in the perfect tense and as a past participle).1 Some dictionaries list smited as an alternative past-tense form.
The adjective smitten, meaning newly (or as if newly) enamored or in love, derives from smite;2 the smitten person has been struck with a figurative blow of love.
Examples
Smite and smote (and smitten in its non-love-related definitions) are usually used in allusions or direct references to the Bible or in text meant to sound archaic—for example:
That’s not what they’ve bargained for in 2012, when the forces of righteousness are due to smite the hated foe and occupy the seats of power. [NPR]
In 2006 the gods of television, too, smote me for some sin I unknowingly committed. [Loyola Phoenix]
She lifted the wooden sword and smote the third party on the head hard enough to split the sword asunder. [Sonoma News]
These writers correctly use smote as the past-tense form of smite. It is occasionally misused in place of smite (e.g., God will smote you).
And although smitten is also a legitimate inflected form of smite, it’s usually used to mean enamored or in love—for example:
He found himself smitten by the sea, the sky and the quality of the light. [BBC]
I’ve been totally smitten by 2009 German rieslings, with their wonderful balance and intensity. [New Zealand Herald]
He’s suitably smitten by a pretty young maiden he meets on the beach (after seeing her in a dream). [AV Club]
As demonstrated in these examples, the correct preposition to follow smitten is by. To say, for example, he was smitten with her technically means that she was used (by something or someone else) to strike him, when in fact she is the one who strikes him.
References
1. http://www.oed.com/view/Entry/182643 ^
2. http://dictionary.cambridge.org/dictionary/british/smitten ^

