I have restartitis and have made countless characters. I have a lot of fun planning out characters and trying to efficiently distribute the perks. This is a list of strategies I came up with to make effective characters without using too many perks. Please add your ideas in the comments.

Conjuration: If you want to be able to summon atronachs or a dremora lord, simply use the atronach forge to make summoning staves or get the sanguine rose. Those are very effective with no perks in conjuration.

Alteration: If you just want to use paralysis, you can also get the paralysis staff at any level and be effective with no perks in alteration. Even with no perks, you can still make use of detect life and dead. It will eat up a lot of magicka, but will give you a few seconds to at least see how many enemies you will be dealing with. You usually use this out of combat, so your magicka has time to recharge.

Illusion: Muffle is something everyone can cast out of combat with no perks.

Restoration: If you have time to run and get some distance, the low level healing spell can still save your life.

Enchanting: With no perks in enchanting you can still get a good boost to stamina, magicka or health regeneration. Take four grand soul gems and pick one of those attributes to enchant armor and jewelery. The percentages add up and you will notice a nice improvement. Muffle and waterbreathing effects are just as good with no perks.

Alchemy: All of these potions are quite effective with no perks: paralyze, invisibility, damage magicka and stamina regeneration, slow. The 50% on slow and 100% on damge regen is always the same whether you have perks or not.

Sneak: still effective with no perks and just taking the 1st perk can really help. For archers at long range in sneak mode, your weapon still does 2x damage. Good for rangers at the start of a battle.

Archery and daggers: Alchemists can use these skills solely as a way to transport poisons to the victim. I had an alchemy character who had no perks in archery, but carried an unsmithed longbow for the sole purpose of shooting poisons from a distance.

Block: Maybe the most effective skill with no perks. One of the good things about shields is that there is a small amount of possible enchantments that can be found on them. It is easy to find or buy a shield with a good block enchantment on it, and the enchantment is usually much stronger than putting perks into shield wall. Finding one of these shields can make you totally effective at blocking with no perks.

Now that I wrote all that, I feel like making a character that uses no perks at all.

Those are some good points. Some of the magic-related ones in particular could help players who want to make a 'traditional' style mage but don't want to spend 60 levels doing it.

When looking at perks, I sometimes look at what perks give you that nothing else can. So for example, Conditioning is superseded by the Steed stone - as long as you don't mind foregoing other Stones. I see Block as offering some utility beyond just damage reduction - Quick Reflexes in particular - so I might take a couple perks there. Of course, it all depends on the character and how many skills are being worked up.