Look at the GT field for the most likely genotype.

For a diploid without multi-allelic loci

grep "^#\|1\/1" snps.vcf > hom-alt.vcf

using my tool vcffilterjs

java -jar vcffilterjs.jar -e 'variant.getGenotype("SAMPLENAME").isHet()' your.vcf.gz > het.vcf

or use isHom() or isHomVar() or isHomRef()

or use GATK variant filtration

snpSift is a useful tool if you want to look at a multisample vcf where all samples should be homozygote (or other types of queries):

for instance for four samples:

java -jar SnpSift.jar filter "countHom() = 4 & !(GEN[0].GT='./.') & !(GEN[1].GT='./.') & !(GEN[2].GT='./.')

& !(GEN[3].GT='./.')" -f my.vcf

It's unfortunate that it considers a no call (./.) also as a homozygote, but the !(GEN[0].GT='./.') ... part deals with that.