I have heard that walkers should be avoided, but what about Excersaucers™ and similar items. Are they safe?
I'm very glad you've heard that walkers should be avoided, as the American Academy of Pediatrics has long urged parents not to use traditional baby walkers, and has even recommended that the US government ban wheeled walkers altogether. This cautionary recommendation is based on compelling injury data. In 1992, there were an estimated 25,700 injuries involving children under the age of 15 months who were treated in US emergency rooms for walker-related injuries.
Wheeled walkers at that time not only allowed children too young to walk on their own to scoot around, turn over, and reach otherwise out-of-reach hazards, but put them at real risk of suffering potentially life-threatening injuries from falls down stairs (or off decks, into pools, etc.). As the numbers of injuries and related concern rose, a voluntary safety standard was put in place in 1997 recommending that walkers have features built in to stop them from moving if their wheels were to go over an edge, thus protecting against stairway falls. While the results were dramatic, with an 88 percent reduction in walker related injuries between 1992 and 2003, wheeled baby walkers that don't conform to the safety standard are still on the market and continue to put young children at risk.
So there's the background on baby walkers for you, which will hopefully give you a healthy respect for the dangers of wheeled walkers. The good news is that it's easy for me to give parents definitive safe and practical advice not to use wheeled walkers because there are plenty of safe alternatives—most notably the stationary activity centers (such as the Excersaucer™) you referenced in your question. These products are designed to allow babies to sit up, stand up, and eventually bounce up and down in a seat surrounded by age-appropriate toys, but without wheels and therefore, without the ability to wheel themselves into trouble.
You will want to be sure and use them according to manufacturer instructions, however. This means not using them for infants that are too young and/or small, for toddlers that are too big and/or tall, or for longer periods of time than your infant is developmentally ready. For a 4-month-old just learning to hold his head upright, this might mean only five to 10 minutes, whereas an 8-month-old expert at sitting already might enjoy sitting upright and playing for considerably longer. That said, do remember that it's important to also allow infants plenty of tummy time and time to freely explore their surroundings.