Before sending your drive to a data recovery service, you need to first consider the question of privacy, and the possibility of damage or loss in transit. You should also attempt to determine whether the problem is a logical one (eg file system damage) or a physical one (board fault or internal damage). Just about anyone should be able to handle a logical data recovery, including the end user. A board problem can in most cases be fixed by the end user, with a little external help if soldering is required. Internal damage, however, requires professional intervention. That said, if the drive has crashed, then 99.99% of data recovery professionals will be incapable of doing anything with your drive. In this case your only real option will be companies such as Kroll Ontrack or Seagate's i365.
In fact the biggest problem is in deciding who to trust from a competence point of view. The data recovery industry is completely unregulated, despite the massive fees that are charged. There is no professional accreditation body, so any ex-IT keyboard puncher or PC board jockey can just hang out his shingle and start offering his services. And that's exactly what happens. These people are mesmerised by dollar signs and the ka-ching of cash registers, so they invest in tools such as PC3000 from Ace Laboratory, Salvation Data's HD Doctor, DeepSpar Imager, Atola Insight, etc.
The formula for success appears to be ...
data recovery wannabe + expensive tool + manual = HDD Guru
Most of these people start out knowing nothing and rely on their tools to do their thinking for them. Some do Scott Moulton's data recovery course, and after only 5 days of tuition they receive Scott's "Data Recovery Expert Certification". Many wouldn't recognise the hot end of a soldering iron and end up outsourcing even the simplest of soldering jobs. At HDD Guru I've had to teach several DR "professionals" how a multimeter works and then show them how to use one. I've had to explain to them how to distinguish between a resistor and a capacitor, even when the resistor was identified with an "R" on the PCB and the capacitor with a "C". I've had to show them how to find a fuse (it is usually near the power source), and how to identify the TVS diodes (a very common problem). I've had to explain to them that the funny numbers on the chips are actually date codes and marking codes, not part numbers. These are all things that every junior technician knows, or should know. The amount of incompetence that I've witnessed at the HDD Guru forums alone should be enough to scare anyone into implementing a rigorous, bullet-proof backup regime.
Some other things I've seen are shorted TVS diodes replaced by wire links (ie a short circuit replaced by a short circuit) and zero-ohm resistors (ie fuses) removed altogether. I've seen quotes of US$850 to remove a HPA (a simple 5-minute job using freeware), $650 for a stiction fault (a 10-minute job involving a little manual dexterity and not much else), and $1400 to remove a shorted protection diode (a $0 DIY fix).
The fact is that many jobs are trivial, but the data recovery profession is able to command such ridiculous fees because they cultivate an aura of mystique via their unwritten code of silence. One reprehensible individual contacted me privately and asked me not to reveal their "secrets". In fact many of the regulars at hddguru.com despise me because I attempt to help those same people that they would like to exploit. I'm the guy in the audience who lifts the magician's black curtain and exposes the wires, pulleys and trapdoors.
As for the question of who to trust, there are some individuals in the DR profession that I respect, both for their integrity and competence, but anyone else would just be a crapshoot.
BTW, on the subject of clear plexiglass covers, be aware that some WD models use a cover screw to retain the head stack. Simply disturbing this screw renders the drive inoperable. DR people claim that it sometimes requires several hours of trial-and-error before they can get the drive working again, and even then the data can only be accessed with difficulty.