http://math.nist.gov/mcsd/Reports/2001/nesf/paper.pdf seems to have a
good bibliography of numerical evaluation algorithms, including
everything from the small-value integer-order case to the
arbitrary-order, arbitrary-argument case.
Of course, that leaves you with the usual problem of smoothness where
you shift from one algorithm to another -- is besselj(1,1) close to
besselj(1+eps,1+delta), where eps and delta are very small complex
numbers....