One-legged Bunk Bed

Bunk beds are surprisingly expensive if you get a sturdy one, and the cheap ones feel pretty flimsy. This one is very easy to build from off-the-shelf lumber, and is rock-solid. Well, at least as solid as your house. This bed was made for my two small boys, but it's strong enough for anyone... as the second picture attests. Try doing that with a regular bunk bed! (actually, don't. It's not very comfortable. Lie on it instead).

Note: this bed worked so well I made two more, this time supported with a combination bookshelf/ladder.

Step 1: Materials

Four 2" x 4" x 10' construction lumber
Four 2" x 4" x 8' construction lumber
Two 4" x 3/4" x 10' finished knotty pine
One 6" x 3/4" x 10' finished knotty pine
One 8" x 3/4" x 10' finished knotty pine
Two 8' x 4' sheets of just about anything - plywood, mdf, particle board, whatever - the mattress sits on it so it could also be slats if you like. I used 1/2" plywood, because I had a project in mind for the offcuts.
3" deck screws
1 1/2" drywall screws
Eight 6" long 1/4" lag screws with washers
Ten 3" 1/4" bolts with nuts and washers
Two 6" 1/4" bolts with nuts and washers
Polyurethane
Wood filler
Sandpaper
You should be able to pick this up for about $150, less if you have some materials lying around.

Step 2: Tools

Cordless drill/driver
Saw (I used a mitre saw and a table saw during this build, but a circular saw or a even a hand saw would be fine)
Level
Tape measure

A router is good for rounding edges, but sandpaper and elbow grease works too.
A studfinder is useful, or you can use Eric's magnet trick.

Step 3: Assemble Frames

Measure the size of the mattresses you're going to use, add some space for bedding (say 1" all round), and you have the dimensions of the frame you need. If you're buying the sheet materials, get the lumberyard to cut it to size on their panel saw. Keep the offcuts for other projects. Screw the 2 x 4's together using deck screws as shown below. Make two of these frames.

Step 4: Add Rails

To one side and one end of one frame, screw the 1 x 6. These screws will show if you fasten in the normal way (thin into thick), so go from the inside out. The drywall screws are not long enough for this job, so predrill bigger holes in the 2 x 4 using a stop on the drill so the drywall screws will go most, but NOT ALL, the way through the 1 x 6. The drill stop can just be a piece of tape. Repeat on the other frame with the 1 x 8.

Step 5: Build Leg

Many commercial beds have 1 x 4 as the legs. This bed is massively overengineered, so you might like to make something lighter weight than the two 2 x 4's I used! 
Screw your two pieces of lumber together lengthways to form an L-shape. Filling the screw holes and sanding will make your bed look nicer. The length should be the same as the height of the top rail in your finished bunk. 
 Note the routed edges in the photo.

Step 6: Fix in Place

Get help for this step. Someone strong and patient is good!
Drill a hole in the leg at the height of the top bunk and into the pre-assembled 8" frame. Drill another hole the depth of the head of your lag screw + washer, and large enough to accommodate the socket. The hole will go through the leg, through the 1 x 8, through the 2 x 4 and into the end grain of the other 2 x 4. Drive in the lag screw.
Find the wall studs, and mark where to drill.
Get someone to stand inside the frame and hold it against the walls in the corner. Use a level to get everything straight! Drill guide holes for the lag screws through 2 x 4, drywall and into the stud. You need a long narrow bit for this. Drive the lag screws through the bed and into the wall. Your helper may now relax.
Repeat for the lower 6" frame.

Step 7: Add Upper Rails

To stop anyone from rolling out of the top bunk, add rails using the 1 x 4's and some short 2 x 4 uprights. Always screw from the inside out as previously done. Leave a gap for the ladder.

Step 8: Build Ladder

You can certainly make less elaborate ladders than the one shown here. This one used a hemlock handrail as rungs and two angled 2 x 3's as uprights. The rungs were attached to the uprights using countersunk 1/4" bolts (see photo). Longer bolts were used for the topmost rung to fix it to the bunkbed. I found the ladder easier to make in place, scribing all the bits I needed to cut. A vertical ladder would have been easier, for sure.

Step 9: Finish

Add the base material and mattresses. Make the beds and you're good to go. You have an incredibly sturdy bunk that will last as long as your kids want it. Because it is all screwed or bolted together, it can be dismantled and rebuilt easily elsewhere.