The bedtools command bedtools genomecov (aka genomeCoverageBed) will do this for you. (The commands below are for version 2.15.0 and above).

By default, you will get a histogram of coverage for each chromosome, and the last group of results will be a histogram of coverage for the genome:

bedtools genomecov -ibam aln.sorted.bam | grep genome

It will also report genome-wide coverage in BEDGRAPH format (only covered intervals):

bedtools genomecov -ibam aln.sorted.bam -bg

BEDGRAPH format with both covered and uncovered intervals:

bedtools genomecov -ibam aln.sorted.bam -bga

Only coverage on the positive strand:

bedtools genomecov -ibam aln.sorted.bam -s +

Scaling coverage by a constant for things like RPM:

bedtools genomecov -ibam aln.sorted.bam -scale 0.73

Taking into account spliced BAM alignments:

bedtools genomecov -ibam aln.sorted.bam -split

Only counting MAPQ >= 30:

samtools view -q 30 -u aln.bam | bedtools genomecov -ibam -

If you want per-base coverage at each base in the genome, you can use the -d option:

bedtools genomecov -ibam aln.sorted.bam -d

samtools will also do this much more quickly, but I believe it will only report positions with coverage > 0:

samtools depth aln.bam