If not using vcftools, the simplest and reasonably fast way is to use awk:

awk 'BEGIN{while((getline<"list.txt")>0)l[$1]=1}/^#/||l[$3]' 1000g.vcf > output.vcf

If you really care about speed, you may use Perl/Python to split the first few fields only instead of wastefully splitting every genotype field. If you do not want to create a temporary file, you can (not recommeded, though):

tabix ftp://ftp-trace.ncbi.nih.gov/1000genomes/ftp/phase1/analysis_results/integrated_call_sets/ALL.wgs.integrated_phase1_v3.20101123.snps_indels_sv.sites.vcf.gz .|awk 'BEGIN{while((getline<"tmp.list")>0)l[$1]=1}/^#/||l[$3]'

You still download the whole file, but does not create a temporary one.

EDIT:

The right way to use grep is:

grep -wFf list.txt output.vcf

we should NOT use just grep -wf. With -F, the patterns are interpreted as fixed strings instead of regular expressions. This will trigger the Aho–Corasick algorithm which is much faster than multi-regex matching. Here is an experiment. tmp.vcf is 1000g site-only VCF on chr20 and tmp.list contains 8582 rs#.

$ time awk 'BEGIN{while((getline<"tmp.list")>0)l[$1]=1}l[$3]' tmp.vcf > /dev/null

real    0m5.318s
user    0m4.365s
sys     0m0.937s

$ time grep -wFf tmp.list tmp.vcf > /dev/null

real    0m2.740s
user    0m1.879s
sys     0m0.768s

$ time grep -wf tmp.list tmp.vcf > /dev/null

(Unfinished. Already 6m50s and counting...)

EDIT 2:

Although grep -wFf is faster, it may give you false matches. For example, if in the INFO field we have FOO=rs1234, a list containing rs1234 will match this line. This scenario rarely happens of course, but you should beware of that.

First, make a file containing the rsid #'s (rsid_list) that you want. Then you can feed this into grep as a list of patterns to match:

grep '^#' 1000genomes.vcf >> slice.vcf
grep -wF -f rsid_list 1000genomes.vcf >> slice.vcf

The first command creates a header from the vcf file. The second command matches patterns given from a file (-f) as word that must be preceded by a non-word character (-w) such as whitespace. We need the last part because you don't want to match rs123456 when you really want rs1234.

Also, you could use:

vcftools --vcf file.vcf --snps rsID.filename --recode --recode-INFO-all

Still need to download the file tho.

You can now also extract such data from the UCSC genome browser's Table Browser. http://genome.ucsc.edu/cgi-bin/hgTables

Group: Variation Track: 1000G Ph3 Vars

Specify a list of variants in rsID format under identifiers.