This one has a lot of cites to it, so it deserves an essay of its own. Solomon Tulbure sets 2 Tim. 1:7 ("God hath not given us the spirit of fear") and 1 John 4:18 ("There is no fear in love") and sets them against about a dozen and a half verses that say to fear God, OT and NT. Let's have a look at these.

In the OT, the word that is overwhelmingly used of "fear" is yare. It does mean "be frightened of" but it also has the meaning of "reverence" or respect. And this is what makes sense in the context of every one of the OT verses Tulbure cites, as in Lev. 25:17: "Ye shall not therefore oppress one another; but thou shalt fear thy God: for I am the LORD your God." What connection would fright have with not oppressing? None -- yare is clearly used in the sense of reverence.

So now, what about NT cites? 2 Tim. 1:7 uses the word deilia, which means timidity; 1 John uses the word phobos, which does mean fright or alarm, but also carries a double meaning, like yare, of fear or reverence. Therefore what is at issue in John is a matter of degree. This is shown in that John speaks in the context of the final judgment: "Herein is our love made perfect, that we may have boldness in the day of judgment: because as he is, so are we in this world." (1:17) The words must be considered to have a shade of meaning, as understood within the linguistic context of Hebrew, which uses "extreme" words to cover a broad range of reactions. (For an example, see here.)