Inner-tube rides (one or two riders) like Malibu Pipeline and Wild Thang let you go by yourself. Larger raft rides like Colossal Curl, Aquazoid, Meltdown, and Big Daddy Falls require groups of two or three to safely run. Usually they will pair you with another group of riders who do not meet the minimum number. Don't quote me on this, but I think Colossal Curl needs at least two and Big Daddy and Aquazoid need at least three? Luckily, 99% of the time the people you get paired with are friendly and it'll be a good experience.
The sign says Big Daddy Falls you can ride alone; however, from experience I have had mixed results. Once I had to have one other person with me at least, another time I swear I rode alone. BTW, riding alone is a bit more thrilling, you really do feel like you might fall out.