I've been using (and been happy with) Axis 2 for a long time. Mostly because when I started working with WS in
Java, there was only Apache
SOAP, from where the road led to Axis 1 and now to Axis 2.
It supports just those standards/protocols I care about (SOAP, WSDL, WS-Security, SAAJ, JAX-WS), and few others, so there isn't a lot of unneeded baggage.
If I were starting out today I'd also look into the Metro stack (which comes with all the bells and whistles), mostly because it seems to evolve by leaps and bounds. Granted, most of those features I might not use, but it'd be interesting nonetheless.