Are Illusion and Alteration helpful? They do not seem nearly as good as Destruction or Conjuration. Do they have more of a purpose other than combat? What are some worthwhile Illusion or Alteration spells?

Didn't use them yet, so other people may help you.
I'm gonna go get a sandwitch.

in other elderscrolls games i'd say yes.. actually game breaking schools of magic imo. However with the loss of many spells from previous games they def dumbed down those 2 schools, i'd have to say no. Fun to mess with I guess? but pointless.

Yes both are great! If you keep an eye on the spoiler forums you would know why.

Depends on how you level them. If illusion is one of your first leveling options the spells might actually do something, but if you leveled with other skills there is a good chance it will be useless until end game because the spells will only effect people far below your level. Alteration, I don't see much value in, it is mostly just a crappy version of armor though it has some small benefits once you get really good at it.

I tend to use Candlelight (illusion) fairly frequently, but as a melee character I rarely use other spells except the occasional summon spell.

If you're a mage (like me) then illusion and alteration is extremely useful. Perks in the alteration tree allows you to absorb magicka and Perks in the illusion spell allows you to cast spells silently (which is useful for dark brotherhood and thieves guild). Also alteration spells that strengthens your armor helps too.

Illusion is helpful if you are going pure mage.