There may be a better solution to your specific red stone contraption you are building, but here are some solutions to get 2 Redstone signals side-by-side.
Redstone dust & opaque blocks
Pro: Has the fastest Redstone travel time
Con:Not directly side by side, have to use Repeaters every 15 blocks
Repeaters
Pro: side by side
Con: not fast, have to use Repeaters every 1 block
Sticky Pistons and Redstone Blocks
Pro:Side by side
Con:Not super slow, but not as fast a Redstone, expensive, makes noise
If you really wanted side by side red stone, you could use commands or mc edit to create Redstone that doesn't connect, just don't update the block. (EDIT: And by don't update the block, that includes no Redstone signals traveling through the Redstone: that updates the block.)
This was done in my red stone test world in Minecraft Pocket Edition, but all the Redstone mechanics shown here work on the PC version as well.