I use Monero for my own purposes. Do I have to update the client after the hard fork or I can use my current one?
Yes, you will need to upgrade.
For the particular HF of 2016-09, maybe not immediately. Note that if you keep the funds in cold storage your funds will still be safe even if you don't do anything now so just holding is safe. However, if you should want to spend them, you would need to use upgraded software.
For example, if you keep them in cold storage for a long time you might skip a few hard forks. Then, to spend, you would just need to install the latest software and import the backup to start spending.
Hard Fork 2016-09 Notes
quoting dEBRUYNE's reddit post:
Not that much will change with the upcoming hardfork, but I figured this thread would be helpful anyway. If you didn't know yet, there will be a hardfork on the 21st of September. Currently, we are on version v2 blocks and with the hardfork we will switch to version v3 blocks. The only (minor) change is that this fork will enforce coinbase transactions to be split in denominations.
Assuming you are on version 0.9.4, you won't have to upgrade your wallet for this fork. That is, no preparation have to be taken for this fork. Note, however, that 0.10 is going to be released soon and in general it is advised to use the latest binaries, because they contain bug fixes and new features. In addition, to prepare for the v4 fork you will have to update to 0.10, because v4 will allow both conventional transactions and Ring CT transactions.
In general, yes you need to update. But not immediately.
After a hard fork you still have 6 months to upgrade (or whatever the period before the next hard fork, might be extended to a year later on).