The commonest modern English greetings are not found in Shakespearean English: hello and hi did not enter the language until the 19th century; and although expressions with how are widespread, they are generally different in form. Greetings may also be different in range of application: good even, for example, might be said any time after noon.

A greeting with an enquiry about health or well-being

cheer TS IV.iii.37 Mistress, what cheer?
how Ham IV.vii.162 How, sweet Queen!
Ham V.i.82 How dost thou, sweet lord?
Ham IV.v.41 How do you, pretty lady?
AYL I.ii.144 How now, daughter and cousin?
TS IV.iii.36 How fares my Kate?
well Ham II.ii.379 Well be with you, gentlemen
TS I.ii.161 you are well met, Signor Hortensio

A greeting with a divine invocation

bless MW II.iii.16 Bless thee, bully doctor!
Ham God bless you, sir
MV II.ii.110 God bless your worship!
mercy KJ I.i.185 God 'a' mercy, fellow [= God have mercy on you (somewhat patronizing)]
save TS I.ii.160 God save you, Signor Gremio
MW II.iii.17 Save you, Master Doctor Caius!
speed R3 II.iii.6 Neighbours, God speed!

A greeting for a time of day

dawning KL II.ii.1 Good dawning to thee, friend
day Tim I.i.1 Good day, sir
Tim III.iv.6 Good day at once [= to one and all]
Tim The good time of day to you, sir
morrow Ham V.i.81 Good morrow, sweet lord!
MW II.iii.19 Give you good morrow, sir
MW II.ii.32 Give your worship good morrow
RJ II.iv.106 God ye good-morrow, gentlemen
even [= evening] AYL V.i.13 Good even, Audrey
AYL V.i.14 God ye good even, William
MW II.i.182 Good even and twenty, good Master Page [i.e. twenty times over]
RJ I.ii.56 Good-e’en, good fellow
RJ I.ii.57 God gi' good-e'en
LLLIV.i.42 God dig-you-den all!
KJ I.i.185 Good den, Sir Richard

A greeting to monarchs

befall R2 I.i.20 Many years of happy days befall / My gracious sovereign
greeting AC V.ii.9 Caesar sends greeting to the Queen of Egypt
hail KL II.iv.122 Hail to your grace
peace KJ II.i.84 Peace be to France
save R2 II.ii.41 God save your majesty
welcome AC II.ii.28 Welcome to Rome

Some of these expressions are also used in leave-taking: FAREWELLS