For the occasional bath (ex. Before a show) I just use Mane and Tail. It's affordable and it works :)
Over the years myself and other riders at our yard use washing up liquid (dish soap). Really good for whitening legs, affordable & we've never encountered with any problems by using it. Hope this was helpful!
I use human shampoo usually Daily Argan Oil, Suave, or Tressemme and during fly season I use Pyrhana Fly Shampoo
I use EQyss shampoo and conditioner. They smell good and they work well.
It' not a "products" but it's very useful, it's the HandsOn Gloves. They are a revolutionary concept that reaches far beyond the traditional curry combs, mitts and shedders on the market today. Wet or dry, they won’t slip or fall off while providing you and your animals with a more thorough and enjoyable bathing and grooming experience.
For products, I use the brand CleanRound. CleanRound horse shampoo kills Bacterium Streptococcus Equi & Fungi. CleanRound horse shampoo is gentle enough to be applied directly to stubborn stains such as grass but effective enough to be diluted in warm water for an all over body wash. It's very useful.