If you are using Excel 2003 or earlier then you are limited to 7 nested functions. If you are using Excel 2007 or later then I think the limit is 64 nested functions.
In VBA, there's no particular limit that I'm aware of, but a lot of And's will be hard to read. Also, if you have a lot of conditions which are time consuming to calculate, it's worth bearing in mind that And statements in VBA (and the AND() function in Excel formulas) do not short-circuit. Let me explain....
Suppose you have a VBA statement like this:
If <condition1> And <condition2> And <condition3> Then
Now, for "Do Something" to happen, all 3 conditions must be True. When each condition is assessed, as soon as one of them returns False then it is pointless to check the others. For example, if <Condition1> is False then there's no need to check <Condition2> or <Condition3>. Unfortunately, VBA And statements are not optimised in this way, meaning that every condition will always be assessed, regardless of what previous conditions have returned. The closest we can get to short-circuiting in VBA is to write separate If statements:
If <Condition1> Then
If <Condition2> Then
If <Condition3> Then
But, depending on the code logic (And/Or etc), this isn't always an option. There are no hard and fast rules here - a lot of stylistic choice.