This is probably the simplest vibrato circuit I've run across. It is based on Tim Escobedo's Wobbletron circuit, but it uses a LED/LDR instead of a JFET for the variable resistance element and the LFO is totally different.
It's definitely on the subtle side of vibe. It's more pitch bendy than it is tremolo-y, and it's hard to hear the effect on low LFO speeds.
This version has a single control: Rate. The LFO depth is set by trimmer, because the sweet spot is very small. There is also an optional switch that adjusts the speed range of the LFO to go from normal to high-speed ring mod and mild octave-down tones.
Just to be clear:
This is NOT a Uni-Vibe clone or workalike. It's simple and subtle, but sounds pretty good I think.
Here is a sound clip I recorded (I was playing the dark, so don't mind the couple clams I hit):
http://soundcloud.com/effdub/wobble-vibe-v1-demoI am working on a more robust version that is deeper and a bit pitchier (and has more parts), but I thought people would enjoy this one as a really simple build or a springboard for a new circuit.
Anyone should feel free to make layouts for this.

Bill of Materials:
R1 1M
R2 2M2
R3 10K
R4 10K
R5 82K
R6 150K
R7 150K
R8 150K
R9 6K8
R10 100R
R11 100R
LDR1 light = ~100R / dark = ~3M (probably anything will work here)
C1 100n
C2 47n
C3 100n
C4 10n
C5 10u
C6 470n
C7 100u
C8 100u
C9 100n
D1 LED (normal diffused LED works fine)
D2 1N4001
IC1 TL072
Q1 2N5089
RATE B50K
SW1 SPDT
TRIM 10K