Was there a change in the reference allele and/or alternate allele for a snp which occurred when a new reference assembly was released or even between builds (e.g. the reference allele in the previous assembly is now the alternative allele in the new assembly)? I am asking specifically for changes from GRCh37 to GRCh38.
A specific thing they looked to do for GRCh38 was identify variants where the reference base was a rare or private allele. Since the genome is made up contigs, all of which are sequenced from real people's genomes and those people have rare or private alleles in their genomes, these will occur in the genome. There are a lot of these in GRCh37 so the GRC sought to fix this. They did this by looking at 1000 Genomes allele frequencies to identify variants, then found short contigs to cover the region where the variant occurs.
Taking Jean-Karim's example variant, here is the genomic region around the variant in GRCh37 and GRCh38. The contig is shown as a bar in the middle of the image in alternating shades of blue. You can see that in GRCh37 the whole region is covered by a contig called AC069356.6, whereas in GRCh38, this same contig occurs but it is split, with a very short contig, KF459701.1, in the middle of it, covering the variant rs4940595.
There are still rare and private alleles in GRCh38, but there are fewer than in GRCh37, and this is why.