Generally no. I've found that some of my buddies from the Army have helped me network and find jobs where I wouldn't have though to look, but I've not encountered a time where I felt like I was rejected because I served in a specific branch.
With that being said, it also depends on what you want to do. If you are more into technology, IT, and computer science, you may want to shop around when you go to enlist and ensure you get the job (MOS in army speak) that you want. You may get feel like you are getting shoe horned into something with a specific branch, reset and try another.