'Think about' is the normal form, probably the only one that non-native speakers need to remember.
As far as I know, 'think on' is mainly archaic, seen only in poetic or literary texts.
... How would you be,
if He, which is the top of judgment, should
but judge you as you are? O, think on that;
and mercy then will breathe within your lips ...
Shakespeare, Measure for Measure, II.iihttp://etext.library.adelaide.edu.au/mirror/c...
Finally, brethren, whatsoever things are true, whatsoever things are honest, whatsoever things are just, whatsoever things are pure, whatsoever things are lovely, whatsoever things are of good report; if there be any virtue, and if there be any praise, think on these things.
Philippians 4:8 (KJV)http://www.biblegateway.com/passage/?search=P...
Lord Jesus, think on me
and purge away my sin;
from earthborn passions set me free,
and make me pure within.http://www.cyberhymnal.org/htm/l/o/lojthink.htm
It survived longer, though, in northern BE dialects such as Yorkshire and Scots.
Think on't, lass, what's Emmerdale when's 't at home?
Think on t mills that we ed then, ah reckan thur musta bin nine-a-ten
My heart it is like for to break / When I think on the days we hae seen
Thir pages micht be mair helpfu gin ye ken a common Inglis wird but ye canna think on the Scots ane for it, but ye aye hiv tae be awaur o the fact as weill
If BE speakers think it's still current, I would guess they might be from the north. (-: