certified (AmE) (recorded delivery in BrE), registered
express
first-class, second-class (both in the UK)
internal (esp. BrE)
If we want to send something to another department, we use the internal mail.

incoming, outgoing
unopened
postal (AmE), regular (esp. AmE), snail (informal, humorous)
air (usually airmail), surface
electronic (usually email), video, voice
direct
direct-mail advertising

bulk
junk, unsolicited, unwanted
I throw away junk mail without reading it.

fan
hate
He has received death threats and hate mail from angry fans.

item, piece
the strange piece of fan mail she'd received two days earlier

sackful

post (BrE), send
get, receive
deliver
forward, redirect (BrE)
We had our mail redirected when we moved out.

intercept, steal
collect
The mail is collected twice a day.

sort
The postcode allows the mail to be sorted automatically.

handle
Some people let their assistants handle the mail.

check
She checked her mail before leaving the hotel.

pick up
open
read
answer, deal with

come, go
Has the mail come yet?

delivery
order
All our products are available by mail order.

message
item
ballot, questionnaire, survey
list
program
system
centre/center, room
carrier, man (usually mailman) (postman in BrE)
The mail carrier didn't deliver the mail on Friday.

drop (AmE)
box (usually mailbox), slot (both AmE) (both letter box in BrE)
coach (BrE), train (esp. BrE), truck (AmE)
fraud
bomb (letter bomb in BrE)

by mail
Send it by registered mail.

in the mail
My reply is in the mail.
Is there anything interesting in the mail?

direct, directly
back, out
Mailing out information can be very expensive.

to
The brochures are mailed direct to members.

Mail is used with these nouns as the object:
ballot, coupon, entry, envelope, letter, package, postcard, résumé