There are many different types of adverb.  Many of them end with an -ly, but this is definitely not the rule: there are words that end with -ly that are not adverbs and many adverbs that do not end with -ly.

So, here are some word sets for you:

Adverbs of manner

These are the adverbs that we most obviously recognise.  They are usually adjectives that have an -ly added:

accidently, angrily, anxiously, badly, boastfully, bravely, brightly, cheerfully, deliberately, dramatically, eagerly, elegantly, enormously, exactly, faithfully, foolishly, fortunately, happily, honestly, hopefully, hopelessly, irritably, jealously, kindly, lazily, obediently, obnoxiously, politely, poorly, quickly, rudely, safely, selfishly, slowly, rapidly, tediously, wearily, wildly 

Adverbs of time

annually, always, eventually, finally, frequently, hourly, never, occasionally, often, rarely, regularly, seldom, soon, sometimes, today*, tomorrow*, usually, weekly, yesterday*, yet

*In "Tomorrow is Monday," then "tomorrow" is a noun. But if you say, "I'll see you tomorrow," it's an adverb.

Adverbs of degree

a bit, absolutely, almost, enough, extremely, fairly, lots, pretty (as in 'pretty happy'), quite, rather, too, very

Adverbial conjunctions (also sometimes called connectives)

and, so, but, or

additionally, also, anyway, finally, furthermore, however, in addition, instead, nevertheless, then, therefore, next, still, when whereas

-ly words that are not adverbs

* There is a mistake in the list above in that yearly can be an adverb.  There are lots of words that are more than one type of speech.