You can place levers on top of redstone blocks, but not on the sides.
You can't place tripwire hooks, ladders or buttons on the sides of redstone blocks.
Edit: added ladders to the list, updated version (it's still present in 13w09c).
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Yes, makes no sense to do that.

Buttons, levers and tripwire hooks power all the blocks they are touching, not only the one they are attached to.

I don't understand what you are trying to say, they allways touch 1 block

Levers, tripwire hooks and buttons power the block they are attached to/touching, but they also power redstone, pistons, lamps, doors,tnt and other blocks below and to the sides... Like this: (R=redstone block, L=lever, .=redstone dust powered by the lever but not the redstone block)
Sideways:
RL.
.
Front:
.L.
.
You could use it to make some circuits smaller.

Ladders also cannot be attached (while they do attach to iron or lapis lazuli blocks) while torches and vines do can.
Speaking of vines, its downgrowth can be blocked with buttons etc - a nice decorative feature IMO.

Ladders, buttons, levers and hooks still cannot be attached to redstone blocks in 13w06a.

Confirmed.

Still needs to be fixed as of 13w09b.

Still in 13w23b

Confirmed for 1.6.1.
Also, this can conceivably be an issue with tripwire hooks (which power at both ends, one of which may not have a redstone block), and even moreso when building decorative structures from redstone blocks and wanting to have ladders (which have no role in redstone whatsoever).

Is this still a concern in the current Minecraft version? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.

Confirmed for 1.6.2.

Confirmed for 1.7.5 and 14w08a

Confirmed for 14w11b

Confirmed for 1.7.9 and 14w17a

I guess it's some kind of intended.
Because the redstone block is nearly handled like a glowstone block
(Chests can be opened when redstone block above (14w20b))
and you can place buttons on glowstone so...

Confirmed for 1.8

Shouldn't they be either be placable on all faces or none, it's common sense

I see no reason why these blocks can't be placed on redstone blocks. Many other blocks, such as redstone wire, torches, and rails all work fine. Please reopen.

@@unknown: If Mojang says something is WAI it is WAI.

Confirmed for 16w15b (at least for ladders). It can't be working as intended, all other ore blocks work and redstone blocks aren't transparent (as you can easily check, it doesn't let light through).

Read 1 comment before yours, @unknown resolved this as intended, if mojang says it's intended, it's intended.

This issue is no longer present, and I suspect it was "fixed" in 1.14 when the faces of full/solid transparent blocks were allowed to support other blocks.
I see no beneficial reason to attach those items to a block that's always powered.