It's not really possible to put a simple number on that without looking at other factors. Basically, what I want:
1. The Wizard should be at some risk of running out of spells in the day, but it shouldn't be the default position.
2. The Wizard should be able to contribute to every encounter, and should be able to cast a spell most rounds. However, his spells shouldn't be encounter-enders in most cases - no more than once per day.
3. I don't necessarily feel that all spells should automatically work, but most spells should have at least some effect. So, "save for half" (or equivalent) should be the default for the overwhelming majority of spells.
4. I quite like the 5e model that an adventuring day has an "encounter budget" - so the party may face one big encounter, lots of little ones, or somewhere in between.
So, assuming 4 encounters of 5 rounds each (on average), the Wizard should probably have about 20 spells (of all levels), probably clustered in 1-3 spell tiers, but should only have 1-2 spells of the most powerful tier.