Both respective (meaning each separately according to its own situation) and its adverbial form, respectively, are often used unnecessarily. The words are called for when the distinction matters, or when not including them could cause confusion—for example:
Glen Mazzara and Adam Fierro complete the line-up, writing episodes five and six respectively. [Digital Spy]
This respectively is useful because it tells us that the two writers are working separately on these episodes rather than collaborating on them. Another example:
Nicole Richie and Khloe Kardashian both spent less than a day there in 2007 and 2008 for their respective drunken driving charges. [AP]
And this respective tells us that these women weren’t somehow jointly charged for drunken driving, but had separate incidents.
But in the following examples, respective and respectively add nothing and may even cause confusion:
Two of his top stars – Kentucky Derby winner Super Saver and Met Mile winner Quality Road, continue to prepare for their respective returns. [NY Daily News]
For men, the proportion of treatment admissions rose from 1.8% in 1998 to 8.1% a decade later; for women, those figures were 3.5% and 13.3%, respectively. [WebMD]
With Communion time approaching at the special Mass on Sunday afternoon, Frank Cona and Nancy McNulty left their respective seats in the front pews and lined up with a few others in the back of Charlotte’s Cathedral of St. Patrick. [Charlotte Observer]
Two earthquakes with magnitudes of 6.9 and 7.3, respectively, struck in the New Britain Region of Papua New Guinea in the southwestern Pacific ocean Sunday, the U.S. Geological Survey reported. [CNN]
Two teams entered, and exited, the All-Star break as the unlikely leaders of their respective divisions, and those two clubs meet up this week at Turner Field. [Gainesville Times]
In each of these cases, respective/respectively could be removed with no loss of meaning.