dba sqlplus

sqlplus -prelim

If you cannot login to the database, for instance due to ORA-00020 maximum number of processes exceeded, then chance exists that you could use the -prelim option.

Documented in note 121779.1 for sqlplus version 10.1 and later :
In some cases, no connections are allowed on the instance (in some ORA-20 situations for example).
As of 10.1.x, there is a new option with SQL*Plus to allow access to an instance to
generate traces.
sqlplus -prelim / as sysdba

Only sysdba connection is possible.
sqlplus -prelim system/manager

SQL*Plus: Release Production on Mon Jul 4 10:38:36 2011

Copyright (c) 1982, 2010, Oracle. All rights reserved.

ORA-24300: bad value for mode

And very little access is granted
SQL> select * from dual;
select * from dual
ERROR at line 1:
ORA-01012: not logged on
Process ID: 0
Session ID: 0 Serial number: 0

You can shutdown abort and then restart your database, instead of rebooting your server where other instances may be running.

This is the ultimate chance before reboot. Before this, consider disconnecting / killing some user session to get a regular sqlplus / as sysdba