The GFF3 site offers a specification document with 1916 feature type categories and their descriptions/definitions.

For example:

[Term]
id: SO:0000188
name: intron
def: "A region of a primary transcript that is transcribed, but removed from within the transcript by splicing together the sequences (exons) on either side of it." [http://www.ebi.ac.uk/embl/Documentation/FT_definitions/feature_table.html]
comment: This term is mapped to MGED. Do not obsolete without consulting MGED ontology.
subset: SOFA
xref: http://en.wikipedia.org/wiki/Intron "wiki"
is_a: SO:0000835 ! primary_transcript_region

Or:

[Term]
id: SO:0000198
name: noncoding_exon
def: "An exon that does not contain any codons." [SO:ke]
subset: SOFA
synonym: "noncoding exon" EXACT []
is_a: SO:0000147 ! exon

Etc.

I suppose the real answer is that it depends on what format of gene annotation data you're working with. Anything goes, so long as people agree to use your standard.

From the top my head: promoters, enhancers, chromatin states, DNA modifications (e.g. methylation), variations (SNPs, CNVs), gene type (e.g. coding/non-coding ...). There's probably more. Just look at annotated genomes in Ensembl to get ideas.