What is this game that's similar to Go?
There are two strong possibilities that are both played on a 19x19 board, Pente and Go Moku. Both have as a goal to get 5 in a row.  Pente also allows capturing and you can win by capturing 5 pairs of stones.

Pente



Pretty good game, I had it confused with Go for the longest time as well.  There have been a bunch of editions over the years, you shouldn't have any trouble finding a set.