We see that -im and -ī tend to be common in the same words. That is, where -im is of frequency, so too is -ī.
- For more on where the -im ending shows up, see this post.
- Beyond the contents of that post, the -ī ablative ending also appears:
Always—
1. with secūrī
2. with the adjectives (nominative -is) where these are used as nouns:
- aequālī (a contemporary)
- annālī (annals)
- aquālī (washbasin)
- cōnsulārī (former consul, member of the consular rank)
- gentīlī (relative)
- molārī (millstone)
- prīmpīlārī (chief centurion)
- tribūlī (fellow tribesman)
(As adjectives proper, they would be aequāle, annāle, etc. in the ablative.)
3. in the ablative of i-stem neuters (animālī, baccārī, etc.)
Sometimes—
1. With the following nouns: avis, clāvis, febris, fīnis, īgnis, imber, lūx, nāvis, ovis, pelvis, puppis, sēmentis, strigilis, turris (definitions)
2. With the following adjectives (nominative -is or -ens) where they are used as substantives:
- affīnī (son-in-law)
- bipennī (battle-ax)
- canālī (pipe)
- familiārī (immediate family member)
- nātālī (birthday, anniversary)
- rīvālī (rival, competitor)
- sapientī (wise man)
- tridentī (trident)
- trirēmī (trireme)
- vōcālī (vowel, vocalist (pl.))
(As adjectives, they would be affīne, bipenne, etc.)
Apparent Exceptions—
- The ablative of famēs (hunger) is always famē (not famī nor fame)
- The case defective māne (morning) is sometimes mānī (the word is found only in the ablative).
- Canis (dog) and iuvenis (youth) always take the ablative -e, never -ī. (contrast with avis, clāvis, etc.)
Latin for Addicts 
This I don’t understand: “As adjectives proper, they would be aequāle, annāle, etc. in the ablative.” Wouldn’t you expect them to end in -i?
The general rule goes like this: second-class adjectives (with some exceptions: vetus, comparatives) have an ablative singular in -i. But when these adjectives are used as nouns to designate a person, the ablative ends in -e.
For example:
a sapientI consule: by a wise consul
a sapientE: by a wise man
I sense that this list is designed (by A&G) to capture all the nouns that appear with the -i ending, while recognize that not all of these nouns denote human subjects (annali, canali, etc.).