I like the feel of the Tunisian stitch (also known as Afghan Stitch) and this is best if used with a long crochet hook because all you do is crochet and appear to be knitting while you actually crochet. Make sense? I personally am breaking rules in various ways with this style and I think it is fascinating to see the results of a pattern you make (as long as you stick with your own broken rule through the whole project.
To prevent your work from curling, use this Tunisian tutorial for left-hander.
NOTE: The creator of the video is not left-handed. Most of her videos are right-handed so don't get too excited if you are a lefty. Be sure to favorite that tutorial if you like it. That is what I am doing with this blog post. :)
My next post will be a list of some crochet or knitting channels that I have noticed a lot of others have commented on how great of a teacher they are. One channel is so good that I took pictures of her video just to flip horizontally so I could see her method as a lefty would. That user is SimplyDaisy and she is great for beginners. Crochet for Absolute Beginners by SimplyDaisy.