I have been tempted to write my own RPG, more specifically a pulp one as I love the genre, but I don't know how many skills I should have. Skills being things like Strength, Boating, Agility, etc. One system I play, ERP, only has 3. Others like Savage worlds have multiples, but they aren't all used. And then there are things like DnD or COC. I do like the 3 attribute idea, but it is too broad for me. I was thinking of having maybe 5 skills under each, for a total of 15 skills. Thoughts, if any?

A note, I am either probably going to make it magic oriented (RunePunk esque) or horror oriented (Early Cthulhu). Or possibly both. I'd like to do a universal pulp game that covers all kinds like space, magic, weird science, blah blah blah. I am more leaning towards Indiana Jones style. Firmly rooted in basic 1920s tomb raiding, plane fights, etc, but there is magic and lore behind mysteries. Weird science and gadgets are cool, but not necessarily what I want, at least for my setting

Well ask yourself what skills are really.

Skills/Attributes/Ratings of any kind are character effectiveness in the game.  The number usually adds to a roll, or determines how many dice you can roll.  The more different skills you have, the more split up and specific character effectiveness can be.  It means that they can be really good at very specific kinds of situations but less effective overall.  The fewer skills you have the more broadly effective each character can be in a wide variety of situations.  Each gives you a different feel.

The first also makes for different characters, while the latter will tend to make them more homogenoous.

Pulp, for me, leans towards the latter situation.  The heros tend to be broadly effective, not usually specialists.  Perhaps you can go with broad abilities with specific specialty schticks for each character.

I'd pick something.  Playtest it.  If it doesn't feel right, tweak it until it does.  I don't think opinions are going to be much help to you.  We don't have your sensibilites. Try them all and see what fits your vision or feel of what the game should do.  Which one do you like most when you play those other pulp games or rpgs in general?

Just as a point of interest take a look at the Danger Patrol beta by John Harper.  Note that all the characters have the same 8(?) or so skills, just different ratings in them.  But they all have special abilities.

A character's profile need not have the typical descriptors of natural abilities, and neither are these lists obligatory; you can easily construct a functional system without them.  You have to ask yourself if things like strength or agility fit your game appropriately.  For example, a game about ship-to-ship combat in outer space certainly wouldn't have use for "dexterity". 

The style of the game should also be considered when constructing a mechanical framework for what defines a character.  In particular, a style predominantly concerned with storytelling may have no need for attributes or skills whatsoever.  On the other end of the spectrum, you can have a game with a pure tactical focus, where the lack of attributes and skills puts everyone on a level playing field.  In lieu of these elements, you can have special powers be the defining traits of a character instead, which would certainly be adequate for a magic-oriented game.

I think what I might do is give maybe 10-12 skills, then stats for health, magic, defense, and movement.
I'll then give some suggestions for archetypes in how you can build a character (i like value pool systems)
And then i'll list spell schools I think. So you can slightly specialize in say, shooting or strength or piloting
But you are going to be generally good at it all
But the spell schools will be more broad and customizable

Leave it to the play group to decide the number of skills they 'should' have? After all, for their own group, they'll know best.

Perhaps write out a skill list as an example, but leave the amount of skills (and what those skills are) up to the individual group to decide.