It deep-ends what you want to achieve.

STUDIO QUALITY:

"Good quality" "normal" photos can easily be obtained with a timer - having a display that allows you to check framing is a bonus. Using a remote shutter release helps heaps. There are after-market wireless releases available for most brands. This is often a "key fob" sized device that you can hide in your hand so it is not seen in the photo.
Using a short shutter delay is useful for self photos. You then don't have to hide your shutter pressing actions or "face". 2 seconds is usually enough. If your camera does not support this some after market wireless releases with built in timers.
A "fully articulated" display such as on the Sony A99 shown here allows you to compose the image from "in front of the lens".

"FOR THE RECORD" PHOTOS

If you are interested in eg trip photography proof-of-life Kilroy-was-here just-for-fun type images then you can get "very reasonable results with a DSLR held at arms length. This takes some practice but if you add a local or 2 or 3 it can be great fun. I am right handed but a std DSLR usually works better reversed at arms length when held in the left hand.

• "How to hold camera" example only. Focus is on camera in mirror. Mirror used here only to show holding arrangement.
  This is far easier and more secure than it appears. Note that dangling camera strap comes from over familiarity - loop it over your arm so that if you do drop the camera the strap will save it. ( (High ISO as flash & mirrors need extra care and this is a quick demo).

That this is what is being done is often obvious once you are aware it is being done, but many people look at the photos without realising.

It is extremely useful to have an articulating LCD that allows you to see the image that you are about to capture BUT you should not look at it as the photo is taken. Below, in image at left subject is looking at LCD above camera and eyes are obviously "not right". Subjects need to look at lens front as photo is taken. Two images at right show that "reasonable results" can be obtained. Aficionados will decry on-camera flash :-).

With multiple people in the image the photographer needs to be at far left (image right) OR the person at image right must be behind your arm. Not a problem but worth noting - eg see top left image below (lady on image right there and in lower left image is my long suffering wife). (Nobody wants to know, but: L2RT2B Malacca, Urumqi, Ningbo, Donguan, Polyfest, Xian, Malacca, Urumqi, Yogyakarta, Urumqi).

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For extra points or in tight or specialist situations - such as hanging off the outside of a speeding train, you can use a short tripod (say 2 feet / 600 mm) with the camera pointing almost "down the legs" and then hold this at arms length and use a timer. eg set focus point, swing camera in, press shutter button, swing out/pose/hold tight to train - click, repeat as required. I find that a 2 second timer is OK for this - holding camera on tripod at arms length for 10 seconds is somewhat demanding.

Two second timer. Small tripod with legs fully compressed, held at arms length. Safety strap advised :-). [Malaysia]. Exposure & focus & white balance - terrible. Memories of occasion - priceless.

FWIW: Imgur stores these images at higher resolution than they are displayed. Windows/GargoyleMail right-click on image and select "Open image in new tab" opens a larger image than is displayed directly. Other OS / Client combinations will presumably do similarly. In this case full accessible image is 2164 x 1410 (compared to about in this case 790 x 515 on my just over HD LCD).

NB - if participating in potentially dangerous acts to acquire your holiday photos, be sure to not lead others astray. The camera at above left is looking in the direction of travel. This is "safe enough" if you do not fall off AND if you avoid trackside obstacles. The young woman who saw me "playing" and came and joined in was oblivious to such dangers and I had to forcefully emphasise how easy it would be to die.