It is always good to have an RDA, Statspack or AWR report to let a database to introduce itself to you :)
Of course usually you will be needing much more information than this, especially related to the developed applications on that database.
This morning one of my colleagues asked how he can get cumulative logins and sessions high water mark for an Oracle database, so below may help;
set linesize 1000
column name format a25
column num_cpus format a10
column db_block_size format a15
column requests_for_data format 999999999999999999
SELECT to_char(open_time,
'DD-MON-YYYY HH24:MI:SS') last_startup,
SYSDATE - open_time days_passed_from_last_startup,
vp1.VALUE num_cpus,
vp2.VALUE db_block_size
FROM v$thread, v$system_parameter vp1, v$system_parameter vp2
WHERE instance = 'bscsdb1'
AND vp1.NAME = 'cpu_count'
AND vp2.NAME = 'db_block_size';
LAST_STARTUP DAYS_PASSED_FROM_LAST_STARTUP NUM_CPUS DB_BLOCK_SIZE
-------------------- ----------------------------- ---------- ---------------
25-MAR-2008 03:24:20 ,459479167 64 8192
SELECT MAX(d.NAME) db_name,
SUM(s.VALUE / (24 * 60 * 60 * (SYSDATE - t.open_time)) + 0.001) tps
FROM v$database d, v$sysstat s, v$thread t
WHERE s.NAME IN ('user commits', 'transaction rollbacks');
DB_NAME TPS
--------- ----------
BSCS 151,125446
SELECT SUM(s.VALUE) requests_for_data
FROM v$sysstat s
WHERE s.NAME IN ('db block gets', 'consistent gets');
REQUESTS_FOR_DATA
-------------------
13120866284
SELECT SUM(s.VALUE) db_time FROM v$sysstat s WHERE s.NAME IN ('DB time');
DB_TIME
----------
639913103
SELECT sessions_highwater FROM v$license;
SESSIONS_HIGHWATER
------------------
5581
SELECT NAME, VALUE FROM v$sysstat WHERE NAME LIKE '%logon%';
NAME VALUE
------------------------- ----------
logons cumulative 1102893
logons current 5434