Why am I seeing "Error: length(rows) == 1 is not TRUE" with ddply?

Probably because you've mistaken summarize for summary (which won't work like you expect in this context). You probably wanted:

ddply(payroll, "PayBasis", summarize,mx = max(NumRate),mn = min(NumRate),avg = mean(NumRate))
        PayBasis      mx      mn     avg
1         Annual 26843.0 26843.0 26843.0
2         Hourly    13.5    13.5    13.5
3 ProratedAnnual 14970.0 14970.0 14970.0

And be sure to look more carefully at the examples in ?summarize and ?ddply.