Updated March 10, 2014.
Written or reviewed by a board-certified physician. See About.com's Medical Review Board.
Yes, some antidepressants can make you gain weight. While different people may respond differently to the same medication, there are certain antidepressants which are more likely to cause weight gain.
The antidepressants which are most likely to cause this side effect are the tricyclic antidepressants, monoamine oxidase inhibitors (MAOIs) and Remeron (mirtazepine). Although the selective serotonin reuptake inhibitors are generally the least likely to cause weight gain, one drug in this class, Paxil (paroxetine), is more often associated with weight gain.
It is not clear why antidepressants can sometimes make people gain weight, although it is thought that perhaps they have some sort of effect of metabolism or appetite. Some do theorize, however, that it may also be that as people begin to feel better their appetite returns and they feel more like eating, causing them to gain weight.
If you experience weight gain with your antidepressant that you find to be troubling, you should discuss this with your doctor. Your doctor can help you decide whether the benefits of your antidepressant outweigh the side effect of gaining weight. If they do, then it's possible you may be able to take steps such as diet and exercise in order to counteract your weight gain. If not, then your doctor may be able to adjust your dose or switch you to a different medication which is not so prone to causing weight gain.
With the exception of the previously mentioned Paxil, most selective serotonin reuptake inhibitors -- such as Prozac (fluoxetine), Zoloft (sertraline), Luvox (fluvoxamine), Celexa (citalopram) and Lexapro (escitalopram) -- do not cause weight gain.
 Prozac in fact, may cause a small amount of weight loss.
Wellbutrin generally has no affect on weight or may cause a small bit of weight loss.
Effexor (venlafaxine), Cymbalta (duloxetine), Desyrel (trazodone) and Serzone (nefazodone) are also antidepressants which do not tend to make people gain weight.
Sources:
Ferguson, James M. "SSRI Antidepressant Medications: Adverse Effects and Tolerability." The Primary Care Companion to the Journal of Clinical Psychiatry. 3.1 (2001). 22.27.
Hall-Flavin, Daniel K. "Can antidepressants cause weight gain?" Mayo Clinic. Mayo Foundation for Medical Education and Research. Accessed: January 26, 2014.
Moore, David P. and James W. Jefferson. Handbook of Medical Psychiatry. 2nd ed. Philadelphia: Mosby, 2004.
Rakel, Robert E. Textbook of Family Medicine. 7th ed. Philadelphia: Saunders Elsevier, 2007.
Ruetsch, O. et. al. "Psychotropic drugs induced weight gain: a review of the literature concerning epidemiological data, mechanisms and management." Encephale. 31.4 Pt 1 (2005): 507-16.
Vieweg, W. Victor R. et. al. "Psychotropic Drug Considerations in Depressed Patients with Metabolic Disturbances." The American Journal of Medicine 121.8 (2008) : 647-55.