By serial number
On most computers with OS X, you can find the serial number by choosing About This Mac from the Apple menu. You can also find the serial number on the surface of your iMac.
Type the serial number into the Check Your Service and Support Coverage page. The resulting screen will show your model.
By part number on the box
You'll find a sticker on the outside of the original iMac packaging that lists the part number. Match your number with one in the listings below to find your iMac model. The XX characters before the slash (/) vary by country, but the rest of the part number will be the same worldwide.
2015
iMac (Retina 4K, 21.5-inch, Late 2015)
Model Identifier: iMac16,2
Number: MK452XX/A
iMac (21.5-inch, Late 2015)
Model Identifier: iMac16,1
Number: MK142XX/A, MK442XX/A
iMac (Retina 5K, 27-inch, Late 2015)
Model Identifier: iMac17,1
Number: MK462XX/A, MK472XX/A, MK482XX/A
iMac (Retina 5K, 27-inch, Mid 2015)
Model Identifier: iMac15,1
Number: M885XX/A
2014
iMac (Retina 5K, 27-inch, Late 2014)
Model Identifier: iMac15,1
Number: MF886XX/A
iMac (21.5-inch, Mid 2014)
Model Identifier: iMac14,4
Number: MF883XX/A
Model Identifier: iMac14,4
Number: MG022XX/A
2013
iMac (21.5-inch, Late 2013)
Model Identifier: iMac14,1
Number: ME086XX/A
Model Identifier: iMac14,1
Number: ME087XX/A
iMac (27-inch, Late 2013)
Model Identifier: iMac14,2
Number: ME086XX/A
Model Identifier: iMac14,2
Number: ME088XX/A
2012
iMac (21.5-inch, Late 2012)
Model Identifier: iMac13,1
Number: MD093XX/A
Model Identifier: iMac13,1
Number: MD094XX/A
iMac (27-inch, Late 2012)
Model Identifier: iMac13,2
Number: MD095XX/A
Model Identifier: iMac13,2
Number: MD096XX/A
2011
iMac (21.5-inch, Mid 2011)
Model Identifier: iMac12,1
Number: MC309XX/A
Model Identifier: iMac12,1
Number: MC812XX/A
iMac (27-inch, Mid 2011)
Model Identifier: iMac12,2
Number: MC813XX/A
Model Identifier: iMac12,2
Number: MC814XX/A
2010
iMac (21.5-inch, Mid 2010)
Model Identifier: iMac11,2
Number: MC508XX/A
Model Identifier: iMac11,2
Number: MC509XX/A
iMac (27-inch, Mid 2010)
Model Identifier: iMac11,3
Number: MC510XX/A
Model Identifier: iMac11,3
Number: MC511XX/A
2009
iMac (21.5-inch, Late 2009)
Model Identifier: iMac10,1
Number: MB950XX/A
Model Identifier: iMac10,1
Number: MC413XX/A
iMac (20-inch, Early 2009)
Model Identifier: iMac9,1
Number: MB417XX/A
Model Identifier: iMac9,1
Number: MC019XX/A
iMac (27-inch, Late 2009)
Model Identifier: iMac10,1
Number: MB952XX/A
Model Identifier: iMac10,1
Number: MB953XX/A
iMac (24-inch, Early 2009)
Model Identifier: iMac9,1
Number: MB418XX/A
Model Identifier: iMac9,1
Number: MB419XX/A
2008
iMac (20-inch, Early 2008)
Model Identifier: iMac8,1
Number: MB323XX/A
Model Identifier: iMac8,1
Number: MB324XX/A
Model Identifier: iMac8,1
Number: MB388XX/A
Model Identifier: iMac8,1
Number: MB391XX/A
iMac (24-inch, Early 2008)
Model Identifier: iMac8,1
Number: MB325XX/A
Model Identifier: iMac8,1
Number: MB393XX/A
Model Identifier: iMac8,1
Number: MB398XX/A
2007
iMac (20-inch, Mid 2007)
Model Identifier: iMac7,1
Number: MA876XX/A
Model Identifier: iMac7,1
Number: MA877XX/A
Model Identifier: iMac7,1
Number: MB199XX/A
Model Identifier: iMac7,1
Number: MB200XX/A
Model Identifier: iMac7,1
Number: MA877XX/A
Model Identifier: iMac7,1
Number: MA876XX/A
iMac (24-inch, Mid 2007)
Model Identifier: iMac7,1
Number: MA878XX/A
Model Identifier: iMac7,1
Number: MB201XX/A
Model Identifier: iMac7,1
Number: MB322XX/A
iMac (24-inch)
Number: MA456XX/A
2006
iMac (20-inch, Late 2006)
Model Identifier: iMac5,1
Number: MA589XX/A
iMac (17-inch, Late 2006)
Model Identifier: iMac5,1
Number: MA590XX/A
iMac (17-inch, Late 2006 CD)
Model Identifier: iMac5,2
Number: MA710XX/A
17-inch iMac (Mid 2006), 1.83 GHz Intel Core Duo
Model Identifier: iMac4,2
Number: MA406XX/A
20-inch iMac (Early 2006), 2.0 GHz Intel Core Duo
Model Identifier: iMac4,1
Number: MA200XX/A
17-inch iMac (Early 2006), 1.83 GHz Intel Core Duo
Model Identifier: iMac4,1
Number: MA199XX/A
20-inch iMac G5 (iSight), 2.1 GHz
Number: MA064XX/A
17-inch iMac G5 (iSight), 1.9 GHz
Number: MA063XX/A
2005
17-inch iMac G5 (Ambient Light Sensor), 1.8 GHz
Number: M9843XX/A
17-inch iMac G5 (Ambient Light Sensor), 2.0 GHz
Number: M9844XX/A
20-inch iMac G5 (Ambient Light Sensor), 2.0 GHz
Number: M9845XX/A
2004
17-inch iMac G5, 1.6 GHz
Numbers: M9248XX/A, M9363XX/A
17-inch iMac G5, 1.8 GHz
Numbers: M9249XX/A, M9823XXA
20-inch iMac G5, 1.8 GHz
Numbers: M9250XX/A, M9824XX/A