Inspired by a post at metal site hessian.org:

The use of motifs and leitmotifs is very frequent in the musical genres of classical and opera, but we can also find some examples of their use in that furious contemporary “classical” brand of sound making we known as heavy metal.

[...]

Motifs have been used in metal music for all of its existence. In fact, the first motif in the history of the genre is the universally recognizable three-note sequence which is the main riff of the song “Black Sabbath” by the band of the same name. What would the rest of the song be without it? Like this trascendental example, motifs are the norm, rather than the exception, in metal.

Couple of very cool examples of recurring motifs in death metal come from Asphyx (intro to the The Rack and the title track) and Sinister (intro to the album Hate and the track Awaiting the Absu). Both times the intros present a portion of a thought then repeats that thought later in the album within a different context.

Motivic writing is a big part of metal. Sometimes its a very definite part of the writing process (Therion’s Beyond Sanctorum – listen to the way new riffs are actually almost always a variation of a preceding riff) other times its implied by the similarity of riff shapes and tonal pallette a band/album uses (Discharge and Ildjarn are good examples of this, but you can also hear it in Slayer, Malevolent Creation and tons of other bands). One other explicit example of motivic metal is Aisling Dhorcha by Beithíoch (main theme occurs in the intro, then the first and last metal tracks are built around it).

The best metal writing like classical is prismatic: it presents several views of similar or the same ideas to create a sophisticated sense of interconnectedness to the whole. Philosophical implications abound.