Jude 1 reads, 'Jude, a servant of Jesus Christ and a brother of James, To those who have been called, who are loved in God the Father and kept for Jesus Christ:' (TNIV). The big debate in this verse is over the phrase ἐν θεῷ πατρὶ ἠγαπημένοις which the TNIV translates 'who are loved in God the Father' (the NASB, ESV, RSV, and NRSV are similar). The NIV translates the phrase 'who are loved by God the Father' (as does the HCSB). The question is on how to best translate 'ἐν in this case, is it 'in' or 'by?' Commentators are split, with Bauckham and Davids following the TNIV and translating it 'in.' Reese and Green go with 'by.'
If you're interested in the argument based on Greek, it follows in the rest of this paragraph. Green claims that the translation 'by' because in this case ἐν plus a dative expresses personal agent. Bauckham and Davids suggest that if Jude wanted to say 'loved by God', there was a much more natural way to do so in this instance. He could have used ὑπὸ instead of ἐν.
There are a couple of other texts that point in the direction of using 'in.' In verse 21 Jude exhorts his readers to , 'keep yourselves in God's love.' 1 John expresses similar ideas of being 'in God' (c.f., 1 Jn 2:24; 3:24; 4:13, 15, 16) as does John 15. Thus there is precedent for the concept of being loved in God.
The difference between the two is significant. If the majority of translations are right (which I think they probably are), then Jude is stressing that we experience God's love through the intimate relationship we have with him as our father. Everything about the verse is stressing this relational aspect, and the preposition serves to intensify it. Before Jude warns the beloved of the judgment awaiting the infiltrators and those who follow them he wants to give them the strongest assurance he can of God's love for them and that the relationship they have with God is still in tact.