This list will be updated with new tested drives. If You don't see Your drive in list, order bios update - You drive will work well with Your U24E.
In Moscow city (Russia): I can flash Your U24E with modified bios for 1000RUR to enable support of SATA-3 drives (i.e. correct drive detection at power-up, wake-up, reboot of Your U24E).
If You are not in Moscow city - You can write request by email firstname.lastname@example.org - I will send bios for $20. Also You can request free limited demo version by email.
I am owner of ASUS U24E since year of 2012. I found what my U24E doesn't detect drives like HDD ST500LT012, SSHD ST1000LM014, HDD HGST HTS725050A7E630 in AHCI mode. In IDE mode laptop doesn't boot with this drives because of read errors.
I googled for this issue and found what other people have same problem with detection of modern drives: https://www.google.com/search?q=asus+u24e+sata+3.
I don't want to buy other drives and test for particular compatibility with my U24E .
So, in march of 2015 I decided to modify bios and to make U24E compatible with drives I bought.
Two months later I did modified version of bios based on original v.2.09. My U24E and U24E of my clients works fine with new drives in AHCI SATA-2 mode (300 Mbytes/sec).
For notebook HDD's with max speed of 120 Mb/s, limit of 300 Mb/s @ SATA-2 is negligible. For SSD speed limit to SATA-2 can be noticeable, but with practical test with some SSDs I got read speed of 259...279 Mb/s & fast access time. So with SSD @ SATA-2 speed U24E works fine & far faster than with original or 7200rpm HDDs.