Recent projects, such as the second phase of the Human Genome Structural Variation Consortium (HGSVC) have produced assemblies. These are linked to from the page for that data collection. These are haplotype resolved assemblies. More details can be found in the accompanying publication.
The 1000 Genomes Project did not create any assemblies from the genome sequence data it generated.
The Gerstein Lab at Yale University created a diploid version of the NA12878 sequence, which is available from the Gerstein website under NA12878_diploid. When used, groups should cite AlleleSeq: analysis of allele-specific expression and binding in a network framework, Rozowsky et al., Molecular Systems Biology 7:522.
You can create a FASTA file incorporating the variants from an individual with a VCFtools Perl script called vcf-consensus.
An example set of command lines would be:
#Extract the region and individual of interest from the VCF file you want to produce the consensus from
tabix -h ftp://ftp.1000genomes.ebi.ac.uk/vol1/ftp/release/20110521/ALL.chr17.phase1_release_v3.20101123.snps_indels_svs.genotypes.vcf.gz 17:1471000-1472000 | perl vcf-subset -c HG00098 | bgzip -c > HG00098.vcf.gz
#Index the new VCF file so it can be used by vcf-consensus
tabix -p vcf HG00098.vcf.gz
#Run vcf-consensus and use --sample to apply sample-specific variants. If not given, all the variants are applied
cat ref.fa | vcf-consensus HG00098.vcf.gz --sample HG00098 > HG00098.fa
You can get more support for VCFtools on their help mailing list.