I'm not sure what the other answers and comments here are referring to. This is possible rather easily. There are two options, both which allow access to low-numbered ports without having to elevate the process to root:
Option 1: Use CAP_NET_BIND_SERVICE to grant low-numbered port access to a process:
With this you can grant permanent access to a specific binary to bind to low-numbered ports via the setcap command:
For more details on the e/i/p part, see cap_from_text.
After doing this, /path/to/binary will be able to bind to low-numbered ports. Note that you must use setcap on the binary itself rather than a symlink.
Option 2: Use authbind to grant one-time access, with finer user/group/port control:
Now execute your command via authbind (optionally specifying --deep or other arguments, see the man page):
authbind --deep /path/to/binary command line args
E.g.
authbind --deep java -jar SomeServer.jar
There are upsides and downsides to both of the above. Option 1 grants trust to the binary but provides no control over per-port access. Option 2 grants trust to the user/group and provides control over per-port access but older versions supported only IPv4 (since I originally wrote this, newer versions with IPv6 support were released).