Singer/songwriters love to sing and play at the same time. Many engineers think this is a lot of trouble because it makes their job harder. I had one guy in the studio who told me an engineer told him it couldn't be done! Amazing!
The person who has the hardest job is the one performing the song. They're the ones who are trying to express something and open up. Since they are always playing and singing when doing a gig or writing a new song, it stands to reason the most comfortable way for them to record would be the same.
I've had great luck with the previously mentioned mid side technique but also using a couple different mics. The Shure SM7 is pretty directional and sounds really good on some voices. If you usually use a condenser on the guitar like a Shure SM81 or and Audio Technica 4033, maybe you've encountered phase problems.
A cool box to correct this is made by Little Labs - it's called the IBP. Infinitely variable phase, not just 180. You can dial in the exact phase location - it's like having the capsules completely lined up. It's also a super over engineered little box - very high quality.