What to Know
Both 'drive safe' and 'drive safely' are fine to use. Flat adverbs—adverbs without -ly—are common in English. Some others are soon in 'see you soon' and fast in 'time goes so fast.' Adverbial safe functions the same way.
Have you ever told a friend to "drive safe"? If you have, there's a good chance that someone corrected you with "-ly!" Perhaps you even corrected yourself. After all, the second thing we learn about adverbs—besides the fact that an adverb is "a word that describes a verb, an adjective, another adverb, or a sentence"—is that they often end in -ly.
But should they? In fact, the adverb safe is what's called a flat adverb. That is, it's an adverb that has the same form as its related adjective—like safe in "drive safe," slow in "go slow," or easy in "take it easy."
Flat adverbs used to be much more common than they are now. In Robinson Crusoe, Daniel Defoe described weather that was "violent hot." In his famous diary, the English writer Samuel Pepys wrote that he was "horrid angry." But most of these adverbs have long since been abandoned. In Middle English, adverbs like these had case endings that distinguished them from their related adjectives, but those gradually disappeared. Eighteenth-century grammarians didn't even identify flat adverbs as adverbs; they considered them adjectives and the adverbial use to be a mistake.
It's these eighteenth-century grammarians that we have to thank for the still-repeated injunction that adverbs end in -ly—and for the sad lack of flat adverbs today. We still have some, but most of them compete with an -ly form: there's slow and slowly, safe and safely, bright and brightly. But then we have tight and tightly, with tight used in a few places tightly is not: "sit tight," "sleep tight." Near and nearly also do different jobs: "the day is drawing near" vs. "it's nearly over."
A few flat adverbs survive without any competition from an -ly version. Fast is one: "time goes so fast," "fast asleep." So is soon, as in "we'll be there soon."
If you're partial to flat adverbs, you can take comfort in the fact that history—and the dictionary—is on your side. You may even decide to ignore the competing -ly versions entire.