What is the max level in Kingdoms of Amalur?

Solution 1:

The maximum level you can gain is 40. This gives you 120 maximum ability points as you get 3 pre-picked ones in the beginning (as pointed out by RavenDreamer) and 3 with each level up.

This can be confirmed by a hands-on preview that appeared on NZGamer Feb. 1st.

Also by this image from the in-game manual:

Solution 2:

While Marcelo's answer does an excellent job of pointing out the maximum level, the lesser half of my question, about the maximum number of ability points, has hereunto remained unanswered.

Strictly speaking, there are many more ways to gain bonus skills than there are to gain bonus abilities (skill books, trainers, etc.).

However, there are two ways to acquire more than the 120 ability points you get from level up.

The first is from epic gems. The Gem of Enlightenment gives up to 15 ability points, and one of the tree specific gems can potentially give up to 25.

The second, is from Purple and Gold armor pieces. Though I don't know what all pieces give the bonus (that is beyond the scope of the question), there are some items, such as the Mercenary's Boots, below, that also give +1 to all abilities in at tree, which means another potential +25.

On the other hand, 120 ability points is already a lot, and you may not wind up interested in half the skills you might be able to unlock (some are even exclusive; chakram and sceptre mastery, for instance). But if you're dead set on maximizing your number of abilities, this'd be the way to do it.