How to generate a list of all dates in a range using the tools available in bash?

If you are on macOS, then date works a bit differently from GNU date. Here's a variant to Tom Fenech's date invocation that supports both GNU and Darwin:

if [ $(uname) = 'Darwin' ]; then
    d=$(date -j -v+1d -f %Y-%m-%d $d +%Y-%m-%d)
elif [ $(uname) = 'Linux' ]; then
    d=$(date -I -d "$d + 1 day")
fi

If you have GNU date, you could do use either a for loop in any POSIX-compliant shell:

# with "for"
for i in {1..5}; do 
    # ISO 8601 (e.g. 2020-02-20) using -I
    date -I -d "2014-06-28 +$i days"

    # custom format using +
    date +%Y/%m/%d -d "2014-06-28 +$i days"
done

or an until loop, this time using Bash's extended test [[:

# with "until"
d="2014-06-29"
until [[ $d > 2014-07-03 ]]; do 
    echo "$d"
    d=$(date -I -d "$d + 1 day")
done

Note that non-ancient versions of sh will also do lexicographical comparison if you change the condition to [ "$d" \> 2014-07-03 ].

Output from either of those loops:

2014-06-29
2014-06-30
2014-07-01
2014-07-02
2014-07-03

For a more portable way to do the same thing, you could use a Perl script:

use strict;
use warnings;
use Time::Piece;
use Time::Seconds;    
use File::Fetch;

my ($t, $end) = map { Time::Piece->strptime($_, "%Y-%m-%d") } @ARGV; 

while ($t <= $end) {
    my $url = "http://www.example.com/" . $t->strftime("%F") . ".log";
    my $ff = File::Fetch->new( uri => $url );
    my $where = $ff->fetch( to => '.' );  # download to current directory
    $t += ONE_DAY;
}

Time::Piece, Time::Seconds and File::Fetch are all core modules. Use it like perl wget.pl 2014-06-29 2014-07-03.

Using GNU date and bash:

start=2014-12-29
end=2015-01-03
while ! [[ $start > $end ]]; do
    echo $start
    start=$(date -d "$start + 1 day" +%F)
done

2014-12-29
2014-12-30
2014-12-31
2015-01-01
2015-01-02
2015-01-03