Well, personally I think that whenever you can have clearly distinguished combat/non-combat spells, you have failed at game design.
It's also better to make stuff with its own quirks and drawbacks than clear and universal utility, so instead of having spells tailored for specific purposes you should have spells doing specific things.
Transportation:
Waterwalking, waterbreathing, levitation, teleportation. Probably passing through walls, although that overlaps with teleporation a bit.
Seems like you have all the TES stuff I'd add covered.
Oh well:
Passing through obstacles has different sorts of limitations than Teleportation. For teleportation you need to have some way of determining destination, so it often has limitations like needing line of sight or needing to have an "anchor" in place which means having to have visited the place, or having to get an object you marked there. Passing through obstacles, OTOH, is inherently short range, but allows you to pretty much go anywhere (limitations could be placed on the nature of obstacles that can be phased through), may confer unique risks (effect/mana running out when you're embedded in solid matter) and has use as stealth mechanics (hiding in a wall while guards pass by).
You can also have freaky modes of locomotion/teleportation - for example being able to teleport only between places with special environmental conditions (like shadows), between specific types objects (like mirrors) and so on.
The magic has to operate on *some* sort of logic, but not necessarily our everyday one. If you manage to come up with something that is easy to formalize and easy to explain using everyday terms, but strikingly different from everyday experience or simple, universal utility, you have an interesting mechanics influencing gameplay in interesting ways.
Also, invisibility, because it isn't worth it to add a special "Stealth magic" category for essentially a single effect.
It's more along the lines of entire set of effects. You can have one for pretty much any sense/means of detection you want to fool. In line with my previous comments, you could make natural drawbacks - for example muffling spell could also silence its target preventing verbal communication and casting, invisibility would leave your eyeballs visible (Quake style), while full invisibility would require some magical perception to allow seeing anything, etc.
You could also have magical disguise, all sorts of illusions and ability to put illusions on objects.
Mind control:
Charm, detect lies, read mind. Probably possession, but it's usually implemented as a combat-only ability. Probably fear/peace spells that let you avoid combat encounters, but that's borderline. Can't think of anything else that doesn't overlap with non-magical diplomacy and thus isn't redundant.
Diplomacy that allows you to do everything mind control does is badly designed diplomacy.
For example you shouldn't be able to ever convince a character to do something that would be obviously detrimental to their goals and against they desires. You shouldn't be able to get them to do something that would undermine whatever pretense you used to make them consider you a friend. With mind control you can get them to do everything.
With mind control you can also have direct control over a character, so for example you could enter an area that would be off-limits to your party and perform all sorts of complex tasks you'd be able to perform yourself if you were there, without the need to actually script the particulars of such interaction.
You could also have ability to create a sleeper ally by mind control - a character that would go about their behavior normally, as driven by their AI and game's scripting, and not recognized as allied with the PC/party up to the point you "wake" them and assume control, then start doing something hostile.
Lastly, you could have partial versions - how about not being able to control someone, but being able to look through their eyes? It gets especially interesting if you implement spells requiring caster to see the target, not necessarily to have unobstructed line of sight between target and their own body, even more interesting if this spell itself worked this way - you could have interesting ways of doing something somewhere you're not supposed to, and equally interesting potential countermeasures.
Divination:
Detect enemies/traps/doors/illusions/whatever, Skyrim's clairvoyance (kinda hard to coin a more generic terms for it), magical maps (although those seem to become obsolete), scouting (wizard's eye and such).
You also have stuff like Skyrim's detect life and detect dead. You can have a lot of different things you might want to detect and it can get interesting if you keep them doing specific things rather than being tailored for specific purposes. For example instead of spell showing up all NPCs or, worse, just the hostile ones, you could have a life detecting spell failing to show undead and all sorts of constructs, dead showing spells showing *all* dead - good luck using it fend off zombies at cemetery and so on.
Environment interaction:
Light/dark, un/lock, disarm, tekekinesis, creating (and dispelling) magic walls, elemental interactions (freezing water, dousing flames etc), weather changes. Theoretically this category should be the one with most opportunities, but in practice only the first three effects are somewhat common.
Stuff like freezing water is a pretty natural non-combat extension of combat magic (it was pretty impressive in old Lands of Lore, BTW).
If your spells generally focus on manipulating properties of objects and forces acting on them it becomes very interesting - for example you can have levitation not as an effect of its own but as negating gravity in either an area or acting upon specific object. From there you could use it as load lightening spell (to the point of even being able to just push massive objects through the air - they'd still have inertia, though) levitation spell (you'd need some magical or physical propulsion, though), disabling spell (just hang a guy in the air), protective spell (rocks fall- NOPE.) and so forth. You could have an opposite spell usable both in combat, when you need something weighted down and so on.
You could have spells changing interaction of an object or character with all sorts of substances, for example make water behave as solid surface (waterwalking) or air (you can run around on the bottom, but you can also fall to your death and can't ascend or descend easily).
In general it's a good idea to cram as much environmental interaction into your magic as you can. You can, for example have, combat or non-combat elemental spells depending on channeling power from a nearby elemental source, you could animate golems (not necessarily ones useful in combat) from all sorts of materials, you could disintegrate certain materials and so on.
Inventory interaction:
Identifying and uncursing items, creating food/water, transmuting metals. Wouldn't put item enchantment here as it's basically crafting.
I'm generally opposed to magically creating anything permanent, because it's just pure, undisguised gamebreaker.
Communication:
Spirit/demon summoning (for communication purposes only), talking to animals etc. Very rarely seen as a mechanic and not a plot point, and even more rare as spells rather than skills. Lots of wasted potential, could be extremely fun if done right.
Communication could also be extremely useful if forced as mechanics for controlling the party while split. For example, imagine that you travel more or less as blob (either actual or at least close enough for the purpose of discussion). Imagine that you can split-off sub-parties and have some planning system that allows you some hands-off control over what characters will be doing.
Now, for actually ordering the sub-party around you either need to approach or auto alert everything that watches or listens in the area - with magical communication you can maintain stealthy link (as long as someone doesn't detect it magically) across great distances. Hell you could even have a variant of see through other's eyes spell working across telepathic link.
Shapeshifting:
Mostly used for combat, if not - than as transportation means (see Lands of Lore 2). Although it could be pretty interesting to use shapeshifting in social situations (i.e. appearing as someone else), but the only game I can think of that does something similar is Star Trail, and only on one or two occasions.
Shapeshifting in general is a useful way of acquiring traits and abilities you don't have.
You can also have spells giving you particular abilities, for example enhancing your senses.
Summoning:
It's possible to have non-combat uses for summons also (see U8). Although this is a tricky mechanic, because if you can have the same abilities as your summons, they become redundant, and if you don't - that limits an already limited spell list.
Well, not exactly. There are natural abilities and traits you generally won't have. A summon other than mindless variety undead or golem should also be, first and foremost an NPC, even if magically coerced to do your bidding. Basically they should be subjected to faction/reputation mechanics, have dialogue and, if coerced to do something strongly against their will continuously rolling will saves to break out of enchantment.
Would you personally want to play a wizard in a game that has no combat spells at all?
Morrowind, System Shock 2. Ok, both have combat spells, and even some quite powerful ones, but they also have a lot of incredibly useful utility stuff.
Also Arcanum, but I haven't played it enough.
