I voted "snowflake", since for some reason that disdain-laden term was chosen instead of just saying "Homebrewed" or "Personal Alterations" to X base system. But that was the vote.
There is nothign "wrong" with the 5e system, as is. Though I share a number of posters' opinions in the spamming/overuse-creating-dullness/"pew-pew"/video game feel of "combat" cantrips. And, the "at-will" of cantrips, in general, is a no go for me regardless of whatever else is done with the magic system.
So, for starters, if/when I am to run a 5e game, the "at-will" component will come out. I am guessing a suitable replacement would be borrowed from our 1e days of cantrip use and say:
Cantrips known stays as is, once you know them, they're known. Use 'em as many or as few times or whatever combinations situations require as you can within your daily [long rest] allotment.
Introduce cantrip level slots equal to "level + Casting Ability modifier" [per long rest]. If a 4th or 5th level caster has, say 10 cantrip slots per day to use minor magic to perform various mundane tasks or tricks, they are going to seem pretty darn magical to anyone. [EDIT to add
![Devious :] :]](http://www.enworld.org/forum/images/smilies/devious.png)
With a bit of creativity and modicum of showmanship, you might not have to use any of your leveled spell slots at all, throwing that much magic around!

[/EDIT]
Clerics & Druids would have their pick of their whole list, as normal. Wizards and warlocks would have to find/learn/choose from their list. All of them at level + casting ability modifier per day. I might be tempted to permit "at will" use of cantrips to Sorcerers. Seems flavor-appropriate and further differentiates them from wizards or warlocks (the bulk of whom's "at will" magic is -I believe as intended and keeping with the flavor- their invocations and "invested" magical abilities from their patrons.)
For "leveled" spell casting, again, I would introduce [to 5e]/maintain from the 2e days, our homebrewed system of spontaneous casting, which is...somewhat similar to 5e-casting is as written. That is, for arcane-users (as the differentiation of arcane/divine/nature magics are a real and present element of my homebrewed world, moreso than the kind of unspoken/understood/"do what you want with it" division of 5e), you learn/prepare your spells as normal. You accumulate your selection as much as you can/want.
The two alterations (aside from limiting cantrips) for Arcane spell-users:
1. Added "spell levels".
You add a number of slots you can cast (within the levels you can already cast) equal to your Casting Ability modifier. So a mage with Int. +3 would be able to add 3 "[spell] levels worth of magic" to their casting slots for the day. Depending on the mage's level, this could be just 3 1st level slots, a 1st and a 2nd level slot, or 1 3rd level slot. These extra slots must be for slot levels you can already cast, e.g. a 1st level wizard can not cast a 3rd level spell simply because they have 3 spell levels worth of magic to add to their allotment.
2. Spontaneous Casting. I would follow casting progression as presented, but the spontaneous casting choices (selecting which spells to use in which slots) would be relegated to your bottom tiers. That is, you have to study/prepare your spells every day, as normal, until you can cast two tiers higher. At which point, your lower tiers become spontaneous castings.
i.e. Our first level mage, as above with +3 slots, [don't have my books with me, so just go with whatever numbers I use here) has 2 1st level slots, by the book, + 3 slots from their Int. mod., for a total of 5 possible castings of their prepared 1st level spells.
At 3rd level, they get 2nd level slots, they continue to choose and prepare spells known by them, as their slots all. The "extra" slots may now be used to add 3 1st level slots or 1 1st and 1 2nd level slots. All must still be prepared to be used.
At 5th level, let's say the Int. mod. has increased to +4, they gain their 3rd level spell slots. NOW, they must still choose prepare their 2nd level spells and their new 3rd level spell(s) and can not cast what is not prepared. Their 1st level slots may be used/filled with whatever 1st level spells they have access to, without preparation. Just choose, as the situations arise, from the magics at your disposal (whether that is "known" or in your spellbook) and use you slots, as normal. No prep necessary for slots two spell levels lower than your highest slot.
So, at 7th level, when 4th level spells are gained, the mage's 1st AND 2nd level spells need not be prepared, but 3rd and 4th must be. And so on.
For Divine casters, in 5e (as well as old school), this is all kind of moot since they have full access to any/all spells on their lists anyway. Though the added spell levels from their casting ability (Wis) would apply as above.
Nature casters in my homebrew/campaign world setting, Druids & Bards as far as 5e is concerned (and Witches, but that's a whole 'nuther can o' rot grubs) are kind of an "in between" thing and I'd have to really see what I wanted to do with them. Generally speaking, Druids lean toward the "access to anything on the list" of a cleric, and Bards lean to "prepared it out of your magical-music" repetoire/songbook of a mage (i.e. If you don't know the right song/lyrics/chords, you can't properly "cast" your magic). So different access points/procedures to rather overlapping spell selections.
Anywho, that's my answer.
Homebrew [snowflake].
But the 5e system as written is perfectly easily playable without alterations at all.