From wikipedia:
"It is difficult to establish how many cents are perceptible to humans; this accuracy varies greatly from person to person. One author stated that humans can distinguish a difference in pitch of about 5-6 cents.
[1] The threshold of what is perceptible also varies as a function of the
timbre of the pitch: in one study, changes in tone quality negatively impacted student musicians' ability to recognize as out-of-tune pitches that deviated from their appropriate values by +/- 12 cents.
[2] It has also been established that increased tonal context enables listeners to judge pitch more accurately.
[3]
When listening to pitches with
vibrato, there is evidence that humans perceive the mean frequency as the center of the pitch.
[4] One study of vibrato in western vocal music found a variation in cents of vibrato typically ranged between +/-34 cents and +/-123 cents, with a mean variation of +/-71 cents; the variation was much higher on
Verdi opera arias.
[5]
Normal adults are able to recognize pitch differences of as small as 25 cents very reliably. Adults with
amusia, however, have trouble recognizing differences of less than 100 cents and sometimes have trouble with these or larger interval
So it would appear that if you plus or minus 3-5 cents, you're pretty much 'in tune'. Unless you're playing a unison, where you can better hear the 'beat' frequencies.