Tripods and ball heads are an absolute necessity for my photography. Pretty much the only time I don’t have them with me is if I am doing street photography.
When it comes to tripods, it is a give and take between size and stability. For travel photography, I give up some stability to save big time on the size and weight. For the ball head though, I am not willing to give up stability for the small difference as a wobbly ball head will kill your frame. Even without the most stable tripod, you should be fine as long as you aren’t shooting in sand or wind.
Tripods
My favorite travel tripod
My favorite tripod for travel is the Oben CT-3565. It is pretty stable and decent quality, but in a tiny package. The legs have four columns that reverse lock so you can fold the ball head inside and fit this tripod in almost any bag. I have been using this tripod pretty heavily for the past few years and really enjoy it. You can see my review here.
The Stable, but Expensive Top-of-the-Line 
Tripod
The Really Right Stuff TVC-34L tripod is the tripod most photographers dream of. Its large size means it isn’t ideal for travel, but if you want the best tripod out there that is going to be the most sturdy, durable and long-lasting tripod you can buy, this is probably it. There is a reason it is the tripod of choice for many professional landscape photographers.
The All-Around Best Tripod
The Feisol Tournament CT-3442 is the favorite tripod of many of my 
photographer friends. It is a really great balance between stability and portability. It is a bit larger than most travel tripods, but still folds up pretty small and is super light. Another big benefit is that it doesn’t have a center column, which is great for shooting low, but also saves some room for travel. The best part, it is half the price of Really Right Stuff.
The Platypod
For ultimate portability during travel, the Platypod Max or Platypod Ultra. I never go on vacation without my Platypod. I have both models, but usually prefer the Max because it is a little more stable for a bigger set up. These small flat bases hold a ball head and let you get the stability of a tripod nearly anywhere you can take a camera. I love them for travel because I don’t always want to haul a tripod out for family outings on vacation.
Ball Heads
Ball heads are so important to stable photography. While many cheaper tripods come with a ball head, they are usually not the best quality (although, I do like the ball head that came with my Oben tripod discussed above). higher end tripods and ball heads are usually sold separately.
Top-of-the-Line
The Really Right Stuff BH-40 is the best tripod money can buy in my opinion, 
and that of many professional photographers. Unfortunately, it has the price tag to show it as well. If you have the money to spend (the RRS tripod and ball head combo will set you back about $1,200), this ball head is super reliable and strong while maintaining light weight.
Budget Option
If you want to save a whole bunch of money on a ball head, I have a lesser known brand that is made in Oregon. I use the Demon DB-44 and really like it. It is heavy duty, high quality and very strong. The only real downside is I find I need to tighten it a bit more than I would expect, but at less than $75, it is the best deal out there on a ball head.