Putting points into every tree, morphing every skill, and maxing out every passive takes about 60 skill points.
By the time I hit lvl 50 i had 121 skill points, without actually bothering to collect every shard in the last 2 zones, doing any dungeons (which reward 1 skill pt for the first time via the quest), or collecting all the skyshards in cyrodill.
I now have access to the other 2 factions and all their skyshards...
Yea, if you really work at collecting skyshards and finishing everything you can, you'll have more than enough skill points to get whatever you want, really.
I plan on putting heavy points into two class trees, near maxxing out two weapon skills, completing one armor skill line and my racial skill line, and i'll still probably have enough points left over to fill two or three crafting trees.
Ok thanks for the answers. So basically I could go full on 4-5 different trees.
No, you can do a lot more than that. It's 20 skillpoints per class line & weapon line. It's 13 skillpoints per armor line. Crafting is 19-24. Then you have the other random skill lines.
As a side note: beware, the more skill points you have, the more gold it will take to respec them (though if you've got 300 skill points you should pretty much have points in everything you want already and then some)
It takes 100g per skill pt to respec all skill points, so thats X amount of skill points + two 0s at the end.