What you are referring to is called multi-linking. It can be done, but it isn't practical for most people. Here's why.
Let's say you have two lines. You plug both in and you're online. The problem is your online with only the first connection and your computer hasn't a clue how to use both at the same time.
There are solutions to this. The best one is an ISP that supports multi-link. Unfortunately, I don't know of any broadband providers that do this. An ISP that supports multi-link will distribute your bandwidth evenly for every request you make.
The second solution is to use multi-link software. The problem is that software cannot split the data evently across the board, it can only split your connection across different requests.
For example, if you download one file at a time, it will only download using your primary connection. However, if you download two files at a time, the software will then download the second file using your secondary connection. I would imagine such software could also isolate web browsing, P2P programs etc... onto one connection and use the other as an auxillary for whatever suits your fancy, but I don't have any experience with multi-link software.