Habeas corpus
You should have the body

Habemus papam
We have a pope

Habent sua fata libelli
Books have their destiny [according to the capabilities of the reader]

Hac lege

With this law

Haec olim meminisse iuvabit
One day, this will be pleasing to remember

Haec ornamenta mea [sunt]
"These are my ornamnets"
or
"These are my jewels"

Haud ignota loquor
I speak not of unknown things

Hei mihi! Quod nulis amor est medicabilis herbis.
Oh me! Love can not be cured by herbs.

Hic abundant leones
Here lions abound

Hic et nunc
Here and now

Hic jacet
Here lies

Hic locus est ubi mors gaudet succurrere vitae
This is the place where death delights in helping life

Hic manebimus optime
Here we'll stay excellently

Hic sunt dracones
Here there are dragons

Hic sunt leones
Here there are lions

Hinc et inde
From both sides

Hinc illae lacrimae
Hence those tears

Hinc itur ad astra
from here the way leads to the stars

Hinc robur et securitas
herefore strength and safety

Historia vitae magistra
History, the teacher of life

Hoc age
Do this

Hoc est bellum
This is war

Hoc est enim corpus meum
For this is my body

Hoc genus omne
All that crowd/people

Hodie mihi cras tibi
Today it's me, tomorrow it will be you

Hominem pagina nostra sapit

It is of man that my page smells

Hominem non morbum cura
Treat the man, not the disease

Homo bulla
Man is a bubble

Homo homini lupus
Man [is a] wolf to man

Homo minister et interpres naturae
Man, the servant and interpreter of nature

Homo praesumitur bonus donec probetur malus
One is innocent until proven guilty

Homo sum humani a me nihil alienum puto
I am a human being; nothing human is strange to me

Homo unius libri (timeo)
(I fear) a man of one book

honestas ante honores
honesty before glory

honor virtutis praemium
esteem is the reward of virtue

honoris causa

for the sake of honor

hora fugit
the hour flees

hora somni
at the hour of sleep

horas non numero nisi serenas
I do not count the hours unless they are sunny

Horresco referens
I shudder as I tell

Horribile dictum
Horrible to say

Hortus in urbe

A garden in the city

Hortus siccus
A dry garden

Hostis humani generis
Enemy of the human race

Humilitas occidit superbiam
Humility conquers pride

Hypotheses non fingo
I do not fabricate hypotheses