0-based programs or file formats:

0-based index is often the convention in computer science

BAM, BCFv2, BED, and PSL formats (https://samtools.github.io/hts-specs/SAMv1.pdf)
IGV (https://software.broadinstitute.org/software/igv/IGV, “the end position is excluded”)
- However, be noted that the display is one-based!. Please see below for comparison between IGV, UCSC genome browser display, and python string handling.
pysam (always 0-based, following convention of Python, http://pysam.readthedocs.io/en/latest/api.html)

e.g.

ATCG
01234 <- coord

beg: 0
end: 3
seq: [0, 4)  # excluding end

1-based programs or file formats:

1-based index may be more intuitive for visualization.

SAM, VCF, GFF and Wiggle formats (https://samtools.github.io/hts-specs/SAMv1.pdf)

e.g.

ATCG
1234  <- coord

beg: 1
end: 4
seq: [1, 4]   # including end (the file formats may still be excluding the end, UNCONFIRMED)

Comparison of IGV, UCSC genome browser and Python string handling

Here, we look at one particular position, chr3:38184488

IGV centers at T

UCSC genome browser also centers at T, showing views with 3x and 10x zoom-out, respectively

Python string handling

In [0]: import pysam
In [1]: fa = pysam.FastaFile('/gsc/www/bcgsc.ca/downloads/tasrkleat-static/on-cloud/hg19.fa')

In [2]: fa
Out[2]: <pysam.libcfaidx.FastaFile at 0x7f622023f828>

# fetch chr3 sequence
In [3]: seq = fa.fetch('chr3')

# seq is a plain python string
In [4]: type(seq)
Out[4]: str

# chr3 length
In [5]: len(seq)
Out[5]: 198022430

# python string is 0-based, so 38184488 actually points to the position 38184489
# in IGV/UCSC
In [6]: seq[38184488]
Out[6]: 'a'

# 38184487 correspond to the visualization above
In [7]: seq[38184487]
Out[7]: 't'

# verify the surroundings, python string slicing convention: excluding end, i.e. [beg, end)
In [8]: seq[38184486: 38184488 + 1]
Out[8]: 'ata'

In [9]: seq[38184485: 38184489 + 1]
Out[9]: 'aataa'

In [10]: seq[38184484: 38184490 + 1]
Out[10]: 'taataat'

In [11]: seq[38184483: 38184491 + 1]
Out[11]: 'ataataata'