Christmas, holiday (AmE)
anniversary, birthday, graduation (esp. AmE), house-warming, wedding
going-away (esp. AmE), leaving (esp. BrE)
unwanted (esp. BrE)
Customers may return unwanted presents in exchange for vouchers.

buy
get, receive
bring sb, give sb, send sb
exchange
At Christmas, family and friends exchange presents.

hand out
Santa Claus handed out presents to the children.

wrap
open, unwrap

present for
a present for my daughter

present from, present to
It's a present to us all from Granny.

make sb a present of sth
My nephew loves this bike so I'm going to make him a present of it.

clearly, well
The arguments were well researched and clearly presented.

attractively, neatly
briefly
The papers are only briefly presented here.

graphically
The results are presented graphically in Figure 2.

orally, visually
The results can be presented visually in the form of a graph.

formally
The launch is to be formally presented to trade partners in early summer.

aim to, attempt to, seek to, strive to, try to
We have tried to present both sides of the debate.

be designed to
Hotel brochures are designed to present the most attractive aspects of the hotel.

fail to
This book fails to present her story in a coherent manner.

as
He likes to present himself as a radical politician.

for
These two techniques are presented for illustration only.

to
He presented the information to his colleagues.

be
remain

ever
the ever present risk of pollution

physically
Simply to be physically present was all that was required.

naturally
Bacteria are naturally present in the environment.

past and present
a list of all club members, past and present

Present is used with these nouns:
century, circumstance, climate, context, crisis, decade, epoch, era, form, generation, impasse, incarnation, inhabitant, occupant, owner, parliament, phase, position, predicament, preoccupation, prime minister, regime, research, situation, state, study, tense, whereabouts, work