I love, love, love Rottweilers. I grew up with the breed, and when our last one passed, I didn't realize just how much I would miss having a Rottie around.
They're super family dogs. Often they gravitate toward one person inparticular, as I think many breeds do, but they adore their whole entire family. They are a breed that needs to be heavily socialized, and if that's done properly, they're very personable, lovely, happy dogs who you should be able to take anywhere and everywhere without a problem. My Rottweilers loved everybody and thought everyone should be their new best friend, but they were also very observant and knew if/when they shouldn't like somebody. Same sex aggression can be an issue in this breed, both male and female, but I think you'll encounter that in the majority of working breeds out there. It's not as common in females as it is males, but it can happen and is something to be aware of. The biggest thing you can do is to make sure you get a dog or puppy with a suitable temperament to go with your current dog's temperament. That doesn't mean you're guaranteed anything, of course, but it's still an important step.
They're active dogs with a lot of versatility to do practically any task asked of them, but I find them pretty easy to live with as far as energy goes as well. Our Rottweilers could go for hours if we kept them that busy, but they were also content to chill out in the house and relax/chew a bone/play with a toy/etc. until we said it was time to do something.
Our girls were very vocal dogs. They liked to talk to us in various grumbles and roos when they were happy or excited, but they were far from barky dogs. They'd alert us to something when warranted, and were quiet after that. They were all very noisy when playing with other dogs. That scared some people who didn't know them, but it was all in play -- they had a lot to say!
I find them to be very easy to train dogs, as long as you're a confident and assertive person around dogs. They can be a bit stubborn, but do love to please and are very biddable with the right motivation. My Rottweilers were 10x easier to train and get focus out of than my Dobermans are. I love that about the breed.
ACL tears (cruciate ligament) seem to be very common in this breed. Our last girl, Echo, tore her cruciate and I've know many other Rottweilers to do the same. Hip Dysplaysia is a big one as well, and Elbow Dysplasia is another concern. My friend who just got her Rottweiler puppy a few months ago (an Ashemburg puppy, actually -- and absolutely beautiful! Her temperament is amazing..) said that she had a very hard time finding a line without elbow issues somewhere in there. Cancer runs rampant in this breed as well, and is what we lost Echo to at a pretty young age. There are more health concerns as well, but those are the ones I hear of most often. Making sure a breeder fully and completely health tests their dogs in this breed is very, very important (as it is with all dogs).
They do shed a lot with that short double coat. People are often surprised at just how much. I constantly brushed our Rotties to try and alleviate some of the hair around our home. They blow their coat pretty badly a couple times a year as well. They also tend to pant a lot. Mine were always really hot in the summer, and even in the winter with the heat running in the house. And they do often snore a bit as well.
I'm sure there is more I could tell you, but that's all I can think of right now. Hopefully a current owner of the breed will chime in as well. I've been without one for 5 years now, so am sure I'm forgetting a few things.