"No space left on device" and "Too many open file" errors

Some of my appliciations gets "No space left on device" and "Too many open file" errors.

Kernel Linux 2.6.18 Centos EL5

# ulimit
unlimited

# sysctl -a |grep file
fs.file-max = 1616310
fs.file-nr = 10048      0       1616310

# lsof -n | wc -l
14186

I have increased file-max.

# sysctl -a |grep file
fs.file-max = 6465240
fs.file-nr = 8128       0       6465240

Errors are still exist.

# df -i
Filesystem            Inodes   IUsed   IFree IUse% Mounted on
/dev/cciss/c0d1p1    2560864   53916 2506948    3% /
/dev/cciss/c0d1p5    103186432    7420 103179012    1% /var
/dev/cciss/c0d1p2    1280000      29 1279971    1% /tmp
/dev/cciss/c0d0p1      50200      35   50165    1% /boot
tmpfs                 193845       1  193844    1% /dev/shm

# df -k
Filesystem           1K-blocks      Used Available Use% Mounted on
/dev/cciss/c0d1p1      9920592   2702068   6706456  29% /
/dev/cciss/c0d1p5    399696092  84475200 294589820  23% /var
/dev/cciss/c0d1p2      4956316    142068   4558416   4% /tmp
/dev/cciss/c0d0p1       194442     11194    173209   7% /boot
tmpfs                  8316692         0   8316692   0% /dev/shm

And error is not a disk space issue actually.

Some other info:

# free
             total       used       free     shared    buffers     cached
Mem:      16633388   15818376     815012          0     107792   14617052
-/+ buffers/cache:    1093532   15539856
Swap:     11477420    2159604    9317816


What is the problem? I can provide other values also.