Runes
Way back when, before English started to be written in the Latin alphabet, it was written in a set of runes called the Anglo-Saxon Futhorc. And in case you weren't aware, runes are cool as hell, so there's some history buffs out there who think it'd be groovy to see if we could still use them.
Since, you know, the version of English that was written in runes was super old and entirely unintelligible to modern speakers. It used sounds we don't have anymore, didn't use sounds that would develop later, and combined sounds in ways we no longer do. There's no widely accepted standard for how to use runes for modern English; there's just a handful of different people who came up with different systems. Heck, one of them is tailored specifically to General American. Begone, LOT!
A common trend among modern runists is to take a very etymological approach to the pursuit. Like, imagine what runic spelling might look like if we'd never stopped using it, and it had evolved along with the language. And yeah, that definitely deserves consideration to at least some degree. Without it, the particular symbols you use may as well be completely arbitrary.
However, among the competing modern rune standards is one that refused to let etymological considerations stop him from making an incredibly solid spelling system. Rune School not only makes spelling almost entirely intuitive, it even extends consideration to other accents. Though consonants don't change much across accents, vowels can be all over the place, but Rune School's system strikes some good compromises, and even ensures ease of learning for non-native English speakers:
One point of this spelling system is that we want common mergers that occur among native English speakers to look similar (FOOT and STRUT merger, for example). But we want mergers that only occur among non-native speakers to not look similar at all (STRUT and PALM). If we made STRUT look similar to PALM, we would only be doing non-native learners of English a disservice by validating their common confusion between these two phonemes.
"Rune School Spelling System," Rune School
Rune School's vowel system has a heavy basis in phonetics and the history of sound changes in English. For example, since PALM used to be an elongated TRAP, that vowel is written as two of the TRAP vowel, though there's also a shortcut rune that represents it with just one character. Indeed, it divides vowels up into a few families of related sounds: KIT, DRESS, TRAP, LOT, FOOT, STRUT, and schwa. Those are the base sounds that can be transformed in various ways to get different sounds. For instance, every single one of them can have the rune for /r/ appended to (or combined with, but more on that later) them to turn them into rhotic vowels. Three of them, like LOT and the aforementioned TRAP, can be lengthened with another copy of themselves to become "long" forms.
That just leaves the diphthongs, like CHOICE and MOUTH, which Rune School analyzes as vowel-glide sequences. So, for example, the FACE vowel is written as DRESS followed by (or, again, combined with) the rune that makes the y sound, and GOOSE is FOOT and /w/. Even FLEECE is formed in this way. Can you guess how?
I find this system very elegant. It's well-organized and holds up to scrutiny from a phonological standpoint. While the relationships between the sounds related to each other in this way will vary in strength based on accent, it's still set up logically and intuitively enough to be a cinch to learn. It manages to build a complete and unambiguous vowel system out of only eight characters for monophthongs.
What's that? Eight? Even though I only listed seven categories a couple paragraphs ago? Yep, that's right. The eighth one doesn't combine with anything to form any new sounds, which is why I didn't mention it above. That's because it's the HAPPY vowel. I go into more detail about this over on the Shavian page, but long story short, having a separate character to represent the unstressed vowel at the end of "happy" comes in very handy. I'd say more, but I'd like to save the surprise for when you see it in action on the Rune School website.
And as a neat little curiosity, every time Rune School's system has a single sound written with two characters, there is always a way to make that into just one. Sometimes, the digraph can be replaced by a single, unrelated rune that served a similar-ish purpose in history, and other times, you can combine the two runes into one with what's called a bindrune: mirror-flip the first one and smush them together. There's historical precedent for runes being used like this, and Rune School revives the tradition in order to make writing and spelling easier.
How does it make spelling easier, you ask? Simple. Suppose an American and a Brit both want to write the word "spar." The American is fully comfortable spelling that rhotic vowel as, well, a rhotic vowel; in Rune School's case, PALM and /r/. But the Brit is a bit more hesitant. Sure, he usually pronounces it like "spa," without any r-like sound, but the r sound would come back if the next word started with a vowel sound. It doesn't seem right to spell the same word in different ways based on context, but it also doesn't feel right to tack on the /r/ rune when he usually doesn't pronounce it.
The solution is to introduce a single rune that represents that rhotic vowel. Instead of one party having to piece two runes together into one that doesn't sound like their combination, people of all accents can look at that single rune and read it as however they pronounce the phoneme it stands for. Bindrunes are an especially cute implementation of this concept, since even though they're single characters, their very form shows how they were derived.
One downside to runes is that they can be a little cumbersome to handwrite; it's about as annoying as writing everything in all caps. Not horrible, but takes a little more effort than lowercase Latin letters. Some runes are much easier to write if you don't worry about preserving hard angles. For instance, I write the schwa rune as a simple, curved loop, rather than the square with tails that you'll see in runic fonts. I journaled in runes for a little while before shifting to Shavian, but I do want to go back to them every now and again, since I find Rune School's spelling system much more pleasant than Shavian's. Sure, it's mostly the same, but the few improvements it does make are huge if you ask me. Not all that surprising, since the guy who runs Rune School is well-acquainted with Shavian himself.
By all means, I encourage you to go explore the Rune School website. It's got in-depth lessons as to how its system works, various blog posts, and more. It even tells you how to install a rune keyboard on your computer or phone, since runes are in Unicode. The website also has links to the other rune systems I briefly mentioned above, if you're interested. I think Rune School's better, though.