Much to my surprise, I have found that the quality (for lack of a better word) of the USB cable is far more important than whether it's a Y-cable with an additional plug for power.
I have tested around 10 different USB cables with a few 2.5" harddrives on my office desktop pc, which is the most finicky pc I have used when it comes to supplied USB power, and most of the USB Y-cables I have bought separately do NOT supply enough power for my most power-hungry drives even when the extra power-only USB plug is connected. But with the same USB port and the same external drive, some other USB cables do supply enough power, regardless of whether the extra power-only USB plug is connected or not.
It's very surprising to me that there should be such a difference in resistance or other electrical properties of these cables, but since I have confirmed it many times with several different USB cables, I have to accept it as fact, and that it's not a question of a few cables being defective.
So if you have trouble powering your external harddrive with an USB cable, you might want to just try another cable.
For maximum compatibility, I have purchased some 250 GB 1.8" USB harddrives (Samsung S1 Mini) which are specified to draw no more than 0.5A from the USB port, and these work with everything I have tried so far.