Why is the horizontal stabilizer forward of the vertical stabilizer on a P-51? Are there other airplanes that are like this?
The primary factor affecting the longitudinal placement of the vertical stabilizer is yaw authority in a spin. From Corke, here is a relevant diagram and description:
As illustrated in Figure 6.10 for a conventional tail, the vertical stabilizer is caught in the wake of the horizontal stabilizer during an uncontrolled spin. This makes the rudder ineffective. The solution for a conventional tail design is to move the horizontal stabilizer either forward or aft of the vertical stabilizer position.
Why did the P-51's designers go with the aft position? It's hard to say given the myriad trade-offs inherent in any aircraft design and without an authoritative source, but as ymb1 points out, yaw authority outside of a spin is likely the answer. The P-51 was designed for maneuverability, so being a relatively small airplane it was beneficial to get as much rudder area and lever arm as possible out of the design.
As far as other aircraft go, it's a matter of how similar you think should qualify. The P-36 and P-40 use a somewhat analogous configuration (and indeed the P-51 was designed with their mission in mind), the A6M (Zero) has an aft tail but without the extended rudder, ymb1 mentions the Cessna 162, a couple of the Zenith airplanes come close, and I'm sure there are more.
(Source) Corsair top, P-51 bottom.
The noticeable difference above is the taller rudder of the P-51.
A taller rudder is needed for a shorter lever arm (distance between empennage and wing) and/or the need for more yaw authority.
And as @Gerry pointed out, another benefit of having part of the rudder below the elevator line is for spin recovery when the horizontal stabilizer is stalled and sending its wake upwards. The alternative is like the Corsair, with the rudder ahead and clear of the horizontal stabilizer.
Is it unique? No, a Cessna is shown below: