The following table is a quick cheat sheet identifying the genomic coordinate conventions used at different sites, file formats, etc. I welcome corrections and additions in the comments. I'll add them to the companion sheet as time allows. A more detailed description of genome coordinate systems can be found in my earlier post. Note that in this table, I consider zero-based, half-open coordinate conventions to be equivalent to space-counted, zero-start and so do not distinguish them in the table.

Name	Resource Type	Chromosome	0 vs 1	Space vs Base	Notes
UCSC Genome Browser	Genome Browser	chr1, chr2, .. chrX, chrY, chrM	1	Base	Note that when zooming in on the genome browser, the positioning of the tick marks appears to use a space-counted, 0-start convention. As discussed here, this is not the intention. To get the 1-based position, the base coordinate corresponds to the tick mark to its immediate right.
NCBI Map Viewer	Genome Browser	1, 2, .. X, Y, MT	1	Base
Ensembl Location Viewer	Genome Browser	1, 2, .. X, Y, MT	1	Base
UCSC BLAT	Web Tool	chr1, chr2, .. chrX, chrY, chrM	1	Base
NCBI BLAST	Web Tool	chr1, chr2, .. chrX, chrY, chrMT	1	Base
UCSC Table Browser	Web Tool	chr1, chr2, .. chrX, chrY, chrM	0	Space	Output formats are all 0-space formats. However, when specifying the region field is 1-base format.
BED Format	File Format	chr1, chr2, .. chrX, chrY, chrM	0	Space
WIG Format	File Format	chr1, chr2, .. chrX, chrY, chrM	1	Base	UCSC's Wiggle Track Format
Galaxy Interval Format	File Format	chr1, chr2, .. chrX, chrY, chrM	0	Space
GFF/GTF/GFF3 Format	File Format	Depends on context	1	Base	Chromosome names depend on resource using the file format
VCF Format	File Format	Depends on context	1	Base	Chromosome just needs to refer to an identifier in a reference genome or can be a contig id. Position 0 and N+1 (where N = chrom length) are used to refer to telomeres.
UCSC Annotation Files	Data File	chr1, chr2, .. chrX, chrY, chrM	0	Space

Special thanks to John DiCarlo's insights and suggestions!