Can we have different spell types besides the basic touch, projectile, and self?
-channeled spells that do their effect over time. aka a beam spell that does small damage every second, or a channeled heal that heals a small amount every second. But it would have a better mana value than single cast over time spells because you can't do anything else while your using that spell.
-a chain attack that hits multiple targets (eg. chain lightning from warcraft 3)
-homing for projectiles (costs more mana per shot)

What other spell types do you think should be in the game?

Combining like spells will give us homing/projectile spells, like the flamethrower with two fire spells equipped.

I recommend that you go listen to the gameinformer todd howard podcast, it will answer a few questions about the game. Here's a quote about the magic system:

Add Timestop! (wishful thinking)

Well there's a dragon shout that slows down time.

Sounds great then....

Now this probably won't happen, especially with how magic is now equipped in a hand rather than able to be cast using a hand carrying a weapon, but I think it would be fantastic to have something like the http://www.tesnexus.com/downloads/file.php?id=16219 mod at the Nexus.
It isn't really well known, but I really enjoyed it with Spellsword type characters, really made me feel like a Combat + Magic specialist rather than a Magic specialist with a sword or a Combat specialist with fireballs.

What it basically is are new spells to be bought in each store that you could cast like an on strike fire enchantment so that your next hit would be imbued with fire magic. There were similar spells that did the same but caused AoE fire damage on hit, then one more fire enchantment spell that you could place on your weapon until cancelled that drained magicka with each hit but also casts fire damage on strike. There were spells for each effect, including an absorb health on strike, force knockback on strike, frost, shock, demoralize, frenzy, etc. So each spell was like delivering an on touch spell through a weapon strike that could be placed before and while in combat.

I'd much rather some spell types like this being included in the enchanting skill than just being able to enchant your weapon a single time with a single enchantment that can't ever be removed. Not likely for them to do this unless they've already done so, but maybe a modder can port Weapon Magic or do something like it if possible.

Yeah, I'd like an overhauled enchantment system that gives you the option of temporary enchantments powered by magicka instead of charge. I just like the idea of being able to channel magic through a weapon.

Enchantment is a spell again, so maybe we'll be able to do just that.