How can I merge files on a line by line basis?

The right tool for this job is probably paste

paste -d '' file1 file2

See man paste for details.

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You could also use the pr command:

pr -TmJS"" file1 file2

where

• -T turns off pagination
• -mJ merge files, Joining full lines
• -S"" separate the columns with an empty string

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If you really wanted to do it using pure bash shell (not recommended), then this is what I'd suggest:

while IFS= read -u3 -r a && IFS= read -u4 -r b; do 
  printf '%s%s\n' "$a" "$b"
done 3<file1 4<file2

(Only including this because the subject came up in comments to another proposed pure-bash solution.)

Through awk way:

awk '{getline x<"file2"; print $0x}' file1

• getline x<"file2" reads the entire line from file2 and holds into x variable.
• print $0x prints the whole line from file1 by using $0 then x which is the saved line of file2.

paste is the way to go. If you want to check some other methods, here is a python solution:

#!/usr/bin/env python2
import itertools
with open('/path/to/file1') as f1, open('/path/to/file2') as f2:
    lines = itertools.izip_longest(f1, f2)
    for a, b in lines:
        if a and b:
            print a.rstrip() + b.rstrip()
        else:
            if a:
                print a.rstrip()
            else:
                print b.rstrip()

If you have few number of lines:

#!/usr/bin/env python2
with open('/path/to/file1') as f1, open('/path/to/file2') as f2:
    print '\n'.join((a.rstrip() + b.rstrip() for a, b in zip(f1, f2)))

Note that for unequal number of lines, this one will end at the last line of the file that ends first.