Maximum path problem using Scala
In terms of algorithm, I think it is best to focus on the answer you are after.  In This case you want the sum, but I notice your result returns the path and the sum.

If you want to focus on the sum think about starting from the bottom, and accessing the best path in terms of the bottom two rows and merging the results up.

Here is an example:

5
12, 3
2, 4, 9
1, 9, 12, 7


merge last 2 lines (lines 3 and 4)

2 + 9, 4 + 12, 9 + 12


merge the next line (line 2 and the merged result of 3 and 4)

12 + (4 + 12), 3 + (9 + 12)


merge the fist line (line 1 and the merged result of the 2, 3, and 4)

5 + (12 + (4 + 12))


some specific observations about your code


If you are going to access an element by index, use an indexed collection like Vector
Consider using fold or reduce instead of recursion with an accumulator
Props for using immutable variables and data structures 


here is a link to my solution to the problem:
https://gist.github.com/dholbrook/6244448#file-euler18-scala