You could do this with the BEDOPS toolkit.

First, convert the datasets into BED files, e.g.:

$ bam2bed < reads.bam > reads.bed
$ gff2bed < annotations.gff > annotations.gff.bed
$ gtf2bed < annotations.gtf > annotations.gtf.bed

BEDOPS tools are written to work with standard input and output streams, so you can use piping to filter annotations for classes of elements, for instance:

$ gff2bed < annotations.gff | grep -w "gene" > genes.gff.bed
$ gtf2bed < annotations.gtf | grep -w "exon" > exons.gtf.bed
...

Then do set or map operations on BED files, e.g. to get all reads that overlap annotations, use bedops --element-of:

$ bedops --element-of -1 reads.bed annotations.gff.bed > justReadsThatOverlapAnnotations.bed

And to get both reads and their associated, overlapping annotations, use bedmap --echo --echo-map:

$ bedmap --echo --echo-map reads.bed annotations.gtf.bed > readsWithAssociatedAnnotations.bed

Note here that set operations return members of the reference set (or subsets thereof), while map operations return elements from both reference and map sets. The documentation goes into more detail about both operations and arguments for each application.

The simplest way would be to convert the GTF/GFF file to a BED format (you lose a lot of information, of course), and then use samtools view -hL regions.bed alignments.bam > alignments_in_regions.sam.

Now having said that, it'd be good to know what you plan to do with the reads as there's likely a better way to do what you actually want.

As Devon mentioned it completely depends on what you are trying to accomplish. Are the regions pretty self-contained or discontinuous? Is the sequence data from an RNA-Seq experiment, where you have to take splice junctions into consideration?

For RNA-Seq I have used both htseq-count</a> and featureCounts to get counts via GTF (I am more consistently using the latter as it takes multiple BAM files as input and the results are the same as htseq). If you have GFF you can convert to GTF using Cufflink's excellent gffread tool.

You can also get counts from a BED file as mentioned above by Devon and Alex, though these (in general) require a little more fiddling (e.g. may require bed12 output). bedtools is what we have traditionally used; not familiar with BEDOPS yet though I may have to give it a try.