Two years ago, as a CA2 who is also boarded in internal medicine, I thought doing a fellowship was kind of a waste unless you truly loved that field. I thought that if you were likeable in residency (which I was), worked hard (which I do), know your $hit (which I do), get very proficient at regional (yup), be comfortable in big cases like trauma, liver transplant, dissections, hearts, etc... (yup that's me) then you could get a good job. Now that I am out in the real world, I have changed my mind on that. It is true that some markets are tighter than others. However, the trend is that you have to do a fellowship nowadays. That is the best advice I can give to any med student thinking about anesthesia. Maybe you are lucky and have some family connection or want to live in an area where there is a huge need for anesthesiologists and can get a decent general gig out of residency, but the vast majority of people do not fit that description.
If you love anesthesia, figure out early which of the fellowships suits you the most: pain, ccm, cardiac, peds. Regional is a waste, do pain instead. The acute pain service is run by the chronic pain guys at my institution. OB is silly unless you want to be at Brigham and Women's doing the highest risk OB cases.
That's my advice.