Despite all that, it's still the case that some ways of writing are clearer and more elegant than others, and some of the shibboleths are worth following for the sake of clarity, elegance and consistency (I'm fairly sure I don't think that just because I'm an editor at the London Review of Books). They're conventions not rules, however, and different conventions apply to different kinds of discourse: constructions that are unacceptable in so-called Standard English and wouldn't find their way into the LRB or the Guardian – a reinforcing double negative, say – are more than fine in other registers (eg "I ain't gonna work on Maggie's farm no more").
Bearing all that in mind, here are nine conventions (the number as arbitrary as everything else) that are more or less worth adhering to, depending on context, though none of them are hard-and-fast rules (and, yes, I have tried to discreetly break most of them in this preamble).
1. Dangling (or unattached) participle "Going to the shops, a dog ran in front of my bike." The dog must have been worried they were about to run out of bones at the bone shop. Dangling participles are best avoided because they can change the meaning of a sentence. And while it's true that most readers will be able to understand what you're getting at, it's still worth saying what you mean. So: "As I was going to the shops" or "On my way".
"Which is appropriate to non-defining and that to defining clauses," HW Fowler wrote in his Dictionary of Modern English Usage (1926). "The dog that ran in front of my bike had floppy ears." "The dog, which had floppy ears, ran in front of my bike." It's often a fine distinction, and was very possibly invented by Fowler, but it can nonetheless be useful. As with dangling participles, it's about saying what you mean.
3. Split infinitive
One of my English teachers once told us that the critic Helen Gardner's last words were: "My dear, try never to split your infinitives." A nurse had asked her: "Would you like me to gently prop you up?" Split infinitives are worth avoiding to keep pedants at bay, but there's nothing actually wrong with them, and a split infinitive is preferable to an inelegant alternative. "To boldly go" is resoundingly iambic, the alternatives – "boldly to go" or "to go boldly" – either flighty or leaden. The rule against splitting infinitives was supposedly invented by Dryden, by analogy with Latin, in which the infinitive is a single word.
Whom is on the way out, and won't be much missed. There's nothing wrong with saying: "Who am I speaking to?" The stiffer formulation "To whom am I speaking?" can be useful if you want to be stiff. But no one would ever say: "Whom am I speaking to?"
5. Ending a sentence with a preposition
Like beginning a sentence with a conjunction, this is always completely fine. As Winston Churchill never actually said, it's the kind of pedantry "up with which I will not put".
6. Due to
The idea that "due to" is wrong, but "'owing to" is OK is bogus. They're both wrong if used to mean "because of" and both OK if used to mean "the result of". "Due to unplanned engineering works, the train to Basingstoke has been cancelled" is a mistake. "The train to Basingstoke has been cancelled; this is due to unplanned engineering works" is fine. Still, "due to" is best avoided because it leads to formulations such as "due to the fact that", which is a really clumsy way of saying "because".
7. Greengrocer's apostrophe
"Carrot's" and "apple's" are not so common, but almost everyone occasionally writes "who's", "it's" and "you're" for whose, its and your. That's the problem with following rules – such as the rule that possessives are distinguished from plurals by an apostrophe – sometimes they don't apply.
8. Different from, not to or than There's no very good reason for following this rule, but then there's no reason not to, either.
9. Using the subjunctive in conditional clauses
And finally, another one that's worth paying attention to, because altering the mood alters the sense. The subjunctive is used to describe a state of affairs that isn't the case. "If the dog were hungry, it would run to the bone shop." This means the dog isn't hungry, as we can tell because it isn't running to the bone shop. "If the dog is hungry, it will run to the bone shop." This means the dog may be hungry, we'll have to wait and see.