Similar meaning, neutral:
* Stir
* Disturb
* Excite
* Provoke
* Rile
* Trouble
* Upset
More negative connotation:
* Incite
* Inflame
* Provoke (stronger)
* Stir up
* Whet (for emotions)
* Antagonize
* Harass
* Bait
* Goad
More specific to emotions:
* Perturb (for anxiety)
* Unnerve (for nervousness)
* Disquiet (for uneasiness)
* Distress (for sadness or pain)
More formal:
* Commove
* Discompose
* Exacerbate
* Foment
The best synonym for "agitate" will depend on the specific situation and the tone you want to convey.