What is a method that can be used to increment letters?

Simple, direct solution

function nextChar(c) {
    return String.fromCharCode(c.charCodeAt(0) + 1);
}
nextChar('a');

As others have noted, the drawback is it may not handle cases like the letter ‘z’ as expected. But it depends on what you want out of it. The solution above will return ‘{‘ for the character after ‘z’, and this is the character after ‘z’ in ASCII, so it could be the result you’re looking for depending on what your use case is.

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Unique string generator

(Updated 2019/05/09)

Since this answer has received so much visibility I’ve decided to expand it a bit beyond the scope of the original question to potentially help people who are stumbling on this from Google.

I find that what I often want is something that will generate sequential, unique strings in a certain character set (such as only using letters), so I’ve updated this answer to include a class that will do that here:

class StringIdGenerator {
  constructor(chars="abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ") {
    this._chars = chars;
    this._nextId = [0];
  }

  next() {
    const r = [];
    for (const char of this._nextId) {
      r.unshift(this._chars[char]);
    }
    this._increment();
    return r.join('');
  }

  _increment() {
    for (let i = 0; i < this._nextId.length; i++) {
      const val = ++this._nextId[i];
      if (val >= this._chars.length) {
        this._nextId[i] = 0;
      } else {
        return;
      }
    }
    this._nextId.push(0);
  }

  *[Symbol.iterator]() {
    while (true) {
      yield this.next();
    }
  }
}

Usage:

const ids = new StringIdGenerator();

ids.next(); // 'a'
ids.next(); // 'b'
ids.next(); // 'c'

// ...
ids.next(); // 'z'
ids.next(); // 'A'
ids.next(); // 'B'

// ...
ids.next(); // 'Z'
ids.next(); // 'aa'
ids.next(); // 'ab'
ids.next(); // 'ac'