Product review (4 stars): ONLY for dwellings that have no venting or washer/dryer hookup
After some initial research into the matter, I found out that you would need a special hookup for either a washer or a dryer (you need both water input and a way to dispose of the dirty water without overflowing your pipes) and you need venting for the dryer.  The majority of machines that were designed to perform in an apartment WITHOUT such a hookup had review after review complaining of poor cleaning, high energy usage, breaking down, noise, super small load capacities, and leakage. But further searching found this LG WM3431 Washer/Dryer with mostly positive reviews on the different websites. It was the answer to my prayers.  (Note:  Despite the negative reviews, you will NOT find a better washer/dryer combo that can operate in an apartment without venting).

The Pros
1.  For apartments --It's one of only a few machines on the market that's designed to work in a small space without a traditional washer or dryer hookup. That means that the electric plug goes into any three-prong outlet in your house and the water input hose can be connected to your sink. The water outlet hose dispenses into any drain and does not dump a huge amount of water so as to overwhelm your sink or bath pipes. The dryer also doesn't need a hot air vent out a window or anything. Of the machines of this genre, I've found that the LG delivers superior performance.
2. Cleaner clothes while using less water. Also, the LG WM3431 has a sanitary cycle that cleans clothes with super hot water and has kept my whites gleaming.
3.  Money --I calculated that at $1.50 per wash and $1.50 per dry, it would cost me $312 a year to do 2 small loads weekly and $468 a year to do 3 small loads weekly.  The machine would pay for itself in two to three years.  That's not to mention the prospect of resale and the time you save yourself from driving to the laundromat and sitting there waiting.
4.  Aesthetic--the machine is beautiful.
5.  Timer-- allows you to load your laundry and detergent before you leave for work and to have it start running and complete its cycle just in time for when you come home. The timer can be set for up to 19 hours later. And since this is an all-in-one machine, you obviously don't need to be home to switch the load from your washer to your dryer.
6. Protects clothing - I only found this out after going on vacation and using a regular washer and dryer for two weeks.  Cheap clothes which I thought were better quality than they actually were, lost probably 1/4 their color during my vacation.  I realized that the steam mechanism of the dryer, though it takes longer, is gentler on clothes than forced hot air.  All my clothing has maintained the color and quality as on the day I bought it, using the LG washer/dryer combo.

The Cons
1.  Time --It takes anywhere from 3-5 hours to do an entire wash and dry, depending on the options you choose.  The spin cycle can add a lot of extra time.  Be mindful of how you load your laundry (i.e. Put one towel on the bottom, some clothes in between, and another towel on top.) If the machine is imbalanced, it will reset and reset and try to balance the load. I've found that if you use only the low spin cycle with the sheet and towel loads, the items will still get sufficiently dry, but the machine will start spinning a lot faster.
2.  Vibration --Others have complained that the machine vibrates violently. I have never had this problem. The machine really does not move or jump at all, even if it's on the very high spin.
3.  Capacity --I can fit a queen fitted sheet, duvet cover, and 4 pillowcases in there, though it's a bit snug. I probably do about 2-3 loads of clothing a week (for a family of 2 adults and 1 toddler), plus an additional load every other week for sheets, towels, and tablecloths. I wouldn't recommend this machine for a much larger family, but I think that there is a larger capacity model available from LG.
4.  Noise --It's actually stealthily quiet during the wash and spin cycles, humming at no louder than your air conditioner. However, the mechanism the machine employs to expel water for your rinse cycles and throughout the long drying cycle is really very loud. Sounds as loud as a car (but maybe not a motorcycle) revving its engine very loudly.
5.  WRINKLES!!--Another major problem is that the way the machine dries, using a condensation method rather than hot air, leaves clothing feeling sometimes damp and often wrinkled when taken out of the machine. My clothes always feels damp when taken immediately from the machine, but 95% of the time, when you spread out the laundry, the steam dissipates and the clothes are actually dry. (Sweaters, jeans, and large items may still be truly damp, unless you've run the machine for very long.) My solution to the wrinkle problem has been to cut my losses and bring extra large items (sheets, tablecloths, dresses, and whatever else MUST be wrinkle-free) down to the basement and just pay to dry it in a regular hot air dryer. My other loads have fared well in the wrinkle department so long as you fill the fabric softener tray to the MAX with fabric softener (I use a non-scented one for this reason) and if you take the clothes out of the dryer as soon as the dry cycle ends. (The dryer continues to run on a "cool-down" mode after it's finished drying, I guess in an attempt to prevent wrinkles, but it causes more wrinkles.)
6.  Door Latch--It keeps the door locked and waits 1-2 minutes before releasing it if you stop the machine mid-cycle and after it's finished drying. So you have to actually wait to pull open the door. I've had instances where I just started the machine and noticed I dropped a sock on the ground and have had to pause the machine, wait 2 minutes, then open up the door and to throw the sock in.
7.  Child Lock--The only thing that changes when you put the child lock on is that it disables the start/pause button and if you turn off the machine, you cannot turn it back on w/o disabling the child lock first. However, the power button still works and the child can turn the machine off in the first place. I cannot tell you how many times my toddler has run over to the washer and turned off my machine mid-cycle by pushing the oooooh! shiny blue colored power button. And I've had to restart the machine (but only after holding down and turning off the child lock) and have the washer begin at the start of the cycle where it left off. It takes extra time this way. And boy is it annoying.
You would think that the least the child lock would keep the door latch locked so that a child cannot climb inside the washer drum. Nope. If the machine is turned off or if it has just completed wash, the door latch will unlock automatically regardless of whether the child lock is on or off. Essentially, the child lock only disables one button on the entire machine. It's pretty much useless otherwise. I wish LG could improve upon this.
8.  BIGGEST DRAWBACK:  Because the WM3431 does not dry clothes using hot air, there is no lint trap.  Then, where does the lint/hair go?  Well, some of it you'll find accumulating in the rubber gasket around the door.  But small amounts of it accumulate in the condenser tube/duct that is INSIDE the machine.  You have to actually disassemble the machine to get to it.  (Yes, this is a major design flaw.)  If your machine starts taking longer and longer to dryer (even longer than 3 hours) or doesn't dry altogether, this could be the problem.  If you're brave of heart, you can disassemble the top and back covers of the machine and find the white plastic duct.  Inside, you'll probably find a mass of lint/hair that's blocking the air from getting to the tub and not letting your clothes dry.  Once removed, your machine will work like new.  You may not want to disassemble the washer/dryer, though, as it could void a warranty.  But some servicemen have said that it is a flaw in this model and recommends clearing these ducts once a year.  I have had the WM3431 for 2.5 years now, and only now did I have to pull it open and clear the lint.  Other ppl may have to do it more often if they have clothes that give off more lint or if they have pets that shed hair.  Annoying?  Definitely yes.  But thank goodness, we got the free extended warranty and a serviceman cleared ducts for us.  I watched him and it really wouldn't be too hard to do it myself, but, yes, it would have been better not to have to do it at all.

Bottom Line:
If you can possibly buy the traditional separate washer and dryer units, by all means, do so!  But if you live in a place where there's no traditional washer/dryer hook-up available, and you're looking to buy, the LG WM3431 is the best choice on the market (ESP. over the Haier models which constantly break down).  Just remember to purchase a (full coverage) extended warranty agreement and keep in mind some of my tips above.  Good luck!