Individually emphasizes the independence of the individuals; separately and severally still more emphatically hold them apart. The signers of a note may become jointly and severally responsible, that is, each liable for the entire amount, as if he had signed it alone.

J. C. Fernald, English Synonyms and Antonyms (1914)

Example sentences

separately Pack the doughnuts and the sandwiches separately.
individually Silverware should be sorted and cleaned individually.
singly I bear in mind that misfortunes never come singly.
respectively Who and who goes where and where, respectively?
independently She'd lived independently since her 18th birthday.

Popularity over time

Word	1850 → 2019	Trend
severally		falling
separately		falling
individually		steady
singly		falling
respectively		steady
independently		steady

Use in printed books, per decade from 1850 to 2019.

By length

5 letters: apart²
6 letters: apiece², singly²
10 letters: separately⁴
12 letters: respectively⁴, individually⁶
13 letters: independently⁵

The small number after each word is its number of syllables (apart² = 2 syllables).