Job for paste:
paste -d, {1,2}.txt
-d, sets the delimiter as ,. {1,2}.txt is brace expansion, done by shell, would be expanded to 1.txt 2.txt.
If you fancy a bit of awk:
awk 'NR==FNR {a[FNR]=$0; next} {print a[FNR], $0}' OFS=, {1,2}.txt
NR==FNR will be true only for the first file; {a[FNR]=$0; next} creates an array a with record numbers as keys, and records as the values
For the second file, {print a[FNR], $0} prints the array element at the corresponding line number followed by current record; OFS=, sets the output field separator as ,
Example:
$ cat 1.txt
1,2,3
4,5,6
7,8,9
$ cat 2.txt
10,11,12
13,14,15
16,17,18
$ paste -d, {1,2}.txt
1,2,3,10,11,12
4,5,6,13,14,15
7,8,9,16,17,18
$ awk 'NR==FNR {a[FNR]=$0; next} {print a[FNR], $0}' OFS=, {1,2}.txt
1,2,3,10,11,12
4,5,6,13,14,15
7,8,9,16,17,18
