I recently built a vertical bike rack from scraps of 2x4s leftover from another project. I built this rack so that the rear wheel from one of our bikes could rest on the floor. I found that I would need this bike to be hung at 63.5" using these hooks, but the wheelbase on this bike is larger than the wheelbase on my other bikes. You can adjust the length of the height (77" for my project) as needed.

The spacing of each bike will be 12", and the top level is 12" higher than the bottom level. If you don't want to alternate the levels to hang each bike, then you will need to accommodate for about 18" of spacing between each bike.

Lengths to cut 2x4s:
2 - 77"
4 - 36"
4 - 28.5"
5 - 15"
2 - 18"
2 - 20"

Screws: 2.5" wood screws

Bike Hooks: Any bike hook system will do, but I picked up these from Home Depot.

Edit: Read this instructable. It is important for the discussion of spacing as well as to see how they did the hooks. One of my bikes rubbed the coating off one hook, so I repaired it with handlebar wrapping and electrical tape.

If you only need to hang one bike, here is my single bike design.

Step 1: Cut Your Wood!

Cut the following lengths of your 2x4s:
2 - 77"
4 - 36"
4 - 28.5"
5 - 15"
2 - 18"
2 - 20"

The 36" lengths are the legs of the stand. Cut a 1.5" x 1.5" corner on one side of each leg.

The 28.5" lengths are the crossbeams. Cut 45 degree corners on both sides of the cross beams (i.e. measure the width of the 2x4 and make the cut extend to the same length of the width).

Step 2: Assemble the Base

Attach the 36" legs to the 77" vertical boards. Unless you are exclusively hanging road bikes, make sure to screw the legs into the shorter sides of the 2x4s in order to leave 3" of clearance for the bike wheels.

Attach one 15" length 2x4 to the 77" vertical boards.

Attach 20" sideboards to the 77" vertical board and 15" base panel on either side of structure.

Attach 15" board to 77" vertical boards and 20" sideboards.

Step 3: Attach Top Supports

Attach 3 supports at the top using the remaining 15" pieces.
The middle support needs to centered at 63.5" to accommodate the height of one specific bike.
The top support is flush with the top of the 77" vertical boards, but its center is is at 75.5".
The lower support is hung at 51.5" in the center, but you can get away with hanging this wherever you feel like, or adding addition supports in the middle of the structure.

Be sure to pre-drill holes to hang the hooks before attaching the top two support pieces.

Step 4: Attach Bike Hooks

Screw in bike hooks to the holes you pre-drilled in the previous step.

Step 5: Attach Crossboards

Attach the 28.5" crossbeams (with 45 degree cuts) to the legs on the bottom as well as the 20" sideboards and 15" support board on top.

Step 6: Attach Support Boards to Legs

Attach two 18" 2x4s to the legs for additional support in order to stabalize the structure. The second 18" 2x4 is necessary so that the derailer from the bike on the lower level does not hit the crossbeams.

Step 7: Enjoy!

I am planning on staining the bike stand so that it matches other things in my apartment, but for now this is a functional bike stand that cost me under $10 (because I had the scrap wood).