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ps u

USER PID  %CPU %MEM    VSZ   RSS TTY  STAT START  TIME COMMAND
akk  3785  0.0  0.0   4188  2088 tty1  S   Jul16  0:00 -tcsh
akk  3885  0.0  0.0   3504  1552 tty1  S+  Jul16  0:00 /bin/bash /usr/
akk  3902  0.0  0.0   2904   820 tty1  S+  Jul16  0:00 xinit /home/akk
akk  3959  0.0  0.0   1868   508 tty1  S   Jul16  0:00 sh /home/akkana
akk  3969  0.0  0.1   9232  4036 tty1  S   Jul16  0:03 xterm -geometry
akk  3971  0.0  0.0   5572  2840 tty1  S   Jul16  0:00 /usr/bin/python
akk  3975  0.0  0.2  12480  7480 tty1  S   Jul16  0:03 openbox
akk  3977  0.0  0.0   3996  2060 pts/0 Ss  Jul16  0:00 -tcsh
akk  3994  0.0  0.0   3140   724 tty1  S   Jul16  0:00 dbus-launch --a
akk  4784  0.0  0.4  28120 13724 tty1  Sl  Jul16  0:03 python /home/ak
akk  6336  0.0  0.1   8796  5536 tty1  R   Jul16  0:00 xterm -geometry
akk  6337  0.0  0.0   4468  2596 pts/1 Rs  Jul16  0:00 -tcsh
akk  8142  0.0  0.5  26408 17180 tty1  S   Jul16  0:06 emacs
akk 10439  0.0  0.0   2704   980 pts/1 R+  11:50  0:00 ps u
akk 24839  0.0  0.1   9676  6004 pts/0 S+  Jul16  0:01 mutt
akk 30568  0.0  0.0   1868   548 tty1  S   Jul16  0:00 /bin/sh /usr/lo
akk 30572  0.1  3.8 266160 120488 tty1 Sl  Jul16  1:01 /usr/local/fire
No, you don't need a minus in front of the u.

With some ps flags, adding a minus changes the meaning completely:
u and -u actually have different meanings.

Note that this is only processes owned by the current user.