On the Categorisation of Hymns
NB: This is intended to be a light-hearted and not entirely serious piece. I do not consider the classification below to be based on far reaching principles or to have great explanatory power.
Hymns(1) are often categorised according to their style of music: old or new, upbeat or staid, intended to be played by organ or by guitar. However, by focusing on the lyrics, an alternative categorisation appears.
Theological. The principal feature of these hymns is that they fit in as much biblical exposition as possible into a few short stanzas. They can either be general, (In Christ Alone; Before the Throne of God Above, And Can it Be) or specific, focusing on one particular event (See, What a Morning - the resurrection; Lo! He Comes with Clouds Descending - the second coming). For the more general ones, a common feature is to focus one verse on each of one of the key parts of Jesus' life (pick four of birth, life, death, resurrection, second coming), as in From the Squalor of a Borrowed Stable or I Cannot Tell. A strong indication that you're listening to a Theological hymn is that they slip a sneaky summary of the Trinity in, usually in the third verse, when you weren't necessarily expecting it ('One with the Father, Ancient of Days/With the Spirit who clothes faith in certainty').
Emotional. These hymns often don't have very many words, or rather the words they do have are repeated frequently. All for Jesus is a very representative example, as is Refiner's Fire. By repetition of a simple yet central message, they focus on the emotional response to that message, rather than seeking to expound theology or discuss more complex matters. I'd also put Taize music into this category.
If you're in an Evangelical church, you can tell whether it's conservative or charismatic by whether or not it has more theological or emotional hymns(2).
Relational. Relational hymns, whilst still often being strongly biblically based, focus much more on the relationship between the singer and God. Unlike Theological hymns, they are less focused on expounding doctrine and more on bringing to life the reaction and response of the ordinary human to God's grace and power. Amazing Grace is a classic of this genre, as is As I Survey the Wondrous Cross or I the Lord of Sea and Sky, but there are plenty of modern examples as well, such as 10,000 Reason or When It's All Been Said and Done. Going back into early history, we find Be Thou My Vision and, even further back, Psalm 23 in an almost archetypal example.
Metaphorical. These hymns aim to invoke a sense of the glory of God in the listener by referencing other, earthly phenomenon. Both Morning has Broken and Hills of the North Rejoice do this, using praise of God's creation to remind the listener of God's greatness, whilst O the Deep, Deep Love of Jesus develops an extensive ocean metaphor. These are the Days of Elijah and Shine Jesus Shine similarly rely on metaphor, though these both use a whole host of metaphors to convey imagery, rather than building a single extended one. I'd also class I Vow to Thee My Country in this category, with its reverse bait-and-switch tactic, pretending to hold up love of country as the greatest love before segueing seamlessly into 'And there's another country...' Some people don't like this style of hymn, and it's true that people who want to choose hymns that mention God as little as possible do choose them, but on the other hand metaphor and imagery can often be a very good way of making a complex matter understandable.
(1) Note that in this piece I use the word 'hymn' to refer to all types of Christian songs regardless of their form; I reject the modern distinction made between Christian 'songs' and 'hymns' as being an unhelpful recategorisation.
(2) This rule is clearly entirely accurate in all circumstances ever.