Today's example comes from Roberto Bolaño's 2666:
Then came an assembly of Germanists in Berlin, a twentieth-century German literature congress in Stuttgart, a symposium on German literature in Hamburg, and a conference on the future of German literature in Mainz. Norton, Morini, Pelletier, and Espinoza attended the Berlin assembly, but for one reason or another all four of them were able to meet only once, at breakfast, where they were surrounded by other Germanists fighting doggedly over the butter and jam.
I absolutely love the "doggedly" there. Of course, I don't know what word was used in the original Spanish, or even if the sentence was constructed in the same way: credit for the adverb must be shared between Bolaño and his translator, Natasha Wimmer. The word just gives the sentence an additional little twist, like fine-tuning a guitar string, that nudges the whole scene into sublimity.
The test of an adverb's necessity is whether the sentence would be the same or stronger without it, and/or if you can find a verb (or, sometimes, adjective) that incorporates the adverb, and becomes more powerful for having consumed it. The image of Germanists "fighting over butter and jam" would still be kind of funny and recognizable. Perhaps "squabbling" or "skirmishing" could be substituted for "fighting," which is not an especially vivid word in itself. But I can't think of a better way to convey the ritualized, determined, petty, hilarious, and hopeless nature of the fight depicted here than with "doggedly." The word gets a boost from the previous sentence, which reflects the relentless march of conferences at which the fight is played out over and over.
But adverbs are the Bigfoot (Bigfeet?) of grammar. They should appear rarely, and be rare and weird themselves. Spotting one should be memorable, and something to tell your friends or blog about.