Biggest key word to me when making these sort of selections is BUDGET. How much are you looking to spend, also how much of a complete system are you looking to build. If you are only looking to add a subwoofer then I personally wouldn't go crazy spending big dollars on a single piece of the puzzle, but if you were going to do speakers and amps then I would look a little more closely at higher end subs to compliment good speakers.
Alpine Shallow 12" - http://www.crutchfield.com/p_500SWRT12/Alpine-SWR-T12.html#details-tab
I would kick this one out just based purely on budget, unless you can find it for a much better price, say around the $300 mark. Spec wise it is pretty similar to the JL 12TW3 other than the power handling, but the JL is a good bit cheaper. also the JL has a pretty good lead on the Fs(Hz) stat (this is basically how low the subwoofer can play with authority.) They are both pretty equal in Xmax and sensitivity.
JL Audio 12TW3 - http://www.crutchfield.com/p_13612TW3/JL-Audio-12TW3-D4.html#details-tab
See above, I would pick this one over the Alpine as your mid to high end selection especially if the Alpine is going to be more money, heck even if the Alpine saves you $50 I would grab the JL, more savings though and the Alpine looks more appealing since they are so close in specs.
Rockford Fosgate P3S-12" - http://www.sonicelectronix.com/item_43416_Rockford-Fosgate-P3SD2-12.html
This is a good budget entry level shallow sub, this gets you up off the bottom feeder subs and into something decent. Stats wise it's a good bit below the JL and the Alpine, RF only has 10mm Xmax vs their 15mm, and a much higher FS rating but if you are only adding a subwoofer and have no plans for amplified door speakers then this is where I would set my target, OR...
Along with the RF sub I would take a good look at the Pioneer offerings. Pioneer was one of the first to enter the shallow market and has always been held in high regard when it comes to budget minded shallow subs.
Pioneer TS-SW3001 12" - http://www.sonicelectronix.com/item_18212_Pioneer-TS-SW3001S4.html
The sensitivity is WAY higher than all the others listed above, this means it will get louder per wattage fed to it, or better utilize the power it's fed. The FS is middle ground, not overly high but would like to see lower. The Xmax is pretty sad, but like I said above Pioneer has always been good and I have heard previous versions of this subs that all sounded and worked good for such a tiny package. Also they recommend a fairly small box compared to the others, previous models were even smaller.
Well after typing all that out for the pioneer and comparing the specs, price being equal between the Pioneer and RF I would have to pick the RF sub.
Now for the
Stereo Integrity BM mkIV - http://stereointegrity.com/index.php?id=47
Now this one is going to be at the upper end of your budget range, similar to the Alpine price wise, but I would compare this more closely to the JL Audio 13TW5, as the 2 pinnacle subs in the shallow mount catagory. The Xmax is much greater than the 13TW5 but actually 1mm shy of the Alpine and the RF sub, it's frequency response starts much lower than the other subs listed and if I had the full T/S specs I would image there are a few other points with the BM looks good.
I don't want to straight pimp this sub as I haven't listened to it yet, but the builder I know is very meticulous when it comes to specs and design and has always put out quality products. I have a previous sub he produced and I will never sell it.
The main difference you will find with this sub is that it is XBL^2 based motor which actually has a distinct different sound compared to common underhung motor design. The best way I can describe the difference is it sounds as if there isn't a subwoofer, it is a cleaner sound that for some is very lacking, but after getting used to it, it is very nice for a SQ system with the sub blending in. Distortion is extremely low, almost non existant, and other specs are more even over the frequency range.
OK, so long story short, depending on your budget, buy the RF if you are looking to stay simple and cheap. Buy the JL if you are looking for a higher end system and hopefully future expansion. Buy the SI sub for the same reasons as the JL if you are willing to do some experimentation and branch out into smaller lesser known gear and hear something a bit different than the norm.