Bitcoin Forum

Can I create my own phrase and turn that into a private key?

Yes. This is like Brainwallet and it is incredibly flawed. The human brain tends to generate weak phrases and it is very easy to exploit.

I was thinkimg of doing it with stuff that is quite personal to me but might not mean much to anyone else. How can I do it?

First of all, DO NOT USE BRAINWALLETS! LOTS OF BITCOINS HAVE BEEN STOLEN FROM THE WEAK AND EVEN SOME HARD ONES!
EVEN THE WORDS FROM AN OBSCURE POEM HAVE BEEN GUESSED - YOU WERE WARNED.

There are two kinds of brainwallets: simple SHA256 (horribly insecure!) and those using a hardened key derivation function.
The hardened ones are way harder to bruteforce and thus are recommended instead of the simple ones.

Brainwallets of the first kind can be generated using bitaddress.org. IT IS STRONGLY RECOMMENDED TO RUN IT OFFLINE ON A LINUX LIVE USB! ALSO, NEVER COPY-PASTE PRIVATE KEYS AND I MEAN IT - FUNDS WERE STOLEN THAT WAY BY MALWARE.
See the warning above, you really don't want to use that way of generating a wallet, even if you're determined to do so.

If you are still sure you have a secure passphrase - personally I'd recommend using WarpWallet: https://keybase.io/warp/warp_1.0.8_SHA256_5111a723fe008dbf628237023e6f2de72c7953f8bb4265d5c16fc9fd79384b7a.html (download the page, run offline, see above).
Make sure to use a salt, and write it down along with the passphrase.
Also, you might want to back that page up in case you'll want to recover your funds later when the site goes down.

Good luck and again, don't use brainwallets. DON'T.