Your question refers to SAM format, but in the event that you may also have a sorted/indexed BAM, you can simply do the following to get this very quickly.

samtools idxstats aln.bam | cut -f 1,3

The solution based on samtools idxstats aln.bam should be used with caution. This is because AFAIK the numbers reported by samtools idxstats (& flagstat) represent the number of alignments of reads that are mapped to chromosomes, not the (non-redundant) number of reads, as stated in the documentation. I stumbled across this by observing that the total numbers reported by samtools idxstats (& flagstat) exceeded the total number of reads in my input fastq files. See further discussion on this issue in the comments on this post: http://left.subtree.org/2012/04/13/counting-the-number-of-reads-in-a-bam-file/

based on the first column only:

awk ' $1 !~ /@/ {print $1}' toy.sam | uniq -c

if you want to count only aligned reads you can also use awk to count only aligned reads.

Here's how I count the number per sequence of primary alignments with proper read pairs: