Sometimes way back in the past I made a magic training spell (or if I had to make 2 perhaps). One spell with an extremely small and harmless effect from each school, small enough that it only cost 1 magicka to cast. The fun thing with combined spells is that they always use the weakest spell school as the "master", so in this case it always trained the school I had the lowest skill in. Very practical if you wan't an all rounder.
A spell I pretty much always make is a 1 magicka (yes, 1 magicka, not 1 point of health) restore health spell. I make it that small since I never take restoration as a minor/major, and a small spell like that is easy to cast for everyone and since I cast it between fights it doesn't matter that I have to cast it 10 times or something. It's actually good since then it also trains my restoration.
A second restoration spell I always make is the restore 1 point agility, strength, endurance.... and so on. That's the same idea as the above. When I have run into a bonewalker or something that have damaged my attributes, I just have to cast that spell a bunch of times and then I'm good to go again. No point having a stronger spell since there is no drawback in casting it several times.
If you are playing as the atronach sign (as I see it, the best sign for every character, even more so for mages), a 17 second (I think it's 17, could be 14 also..) spell of summon ancestral ghost is great. After you have summoned it, punch it 2 or 3 times and he will attack you, filling up your magicka without harming you. 17(14) seconds is the perfect length since it is cheap and he has time to cast two attack spells at you but disapears before he goes at you with his fists.
A 100 point, 1 second resist magicka spell is a classic for everyone who uses the boots of blinding speed. Or 50 if you are a breton.
Those are some of my specials. Other than that, If I play a mage I always make a bunch of different fire/frost spells of different strengths for different enemies. Fire and frost are the only elemental spells needed, but you will have to learn which creatures/races that resists one of them.
A couple of different open lock spells, often 25, 50, 75, 100 points both touch and range so that I can stand around a corner and open a lock without anyone seeing me.
The thing to think of about spells is the duration and points about the spells and therefore how much magicka they cost. Most (almost all) of the purchased spells are quite badly made, especially when it comes to duration. 60 seconds for the conjuration spells? Way, way, way to much. The opponent has either died long before that or your summon have. That's a lot of wasted magicka.
When it comes to spellmaking i always look closely to the magicka cost. Where do I get the most bang for the buck. As with my ancestral ghost for instance, at 18 (or 15) seconds it will cost one more point of magicka, so it's better to stop at 17 (or 14).