Woke up this morning (J.J. Cale)

kicks off with: E... A G E

For the vocal parts, it is just G and E, G and E, G and E...
[G]I woke up early this [E]morning
etc.

Then for the rest it sounds like just E (bass line is something like E E A B   E E A B)

Santa Cruz (J.J. Cale)

This goes approximately like this:
Em | G A | ... endlessly.


Except for the "Well we didn't play long it booed too soon" part:

[A]we didn't play long it [Em]booed too soon

etc.

ending with:

[A]I thought we had played his [Em]favorite song[B]

Wish I Had Me A Dollar (J.J. Cale)

This  simple number only to be found on the multiple disc collections, AFAIK. Like The 3CD Collected or the 2CD Anthology.

This one's a 12-bar blues in D:
DDDD
GGDD
AGDD

Again, most eveident through the V-I bass line.

The solo takes off going back and forth between C and A notes (on the B-string 13th and 10th fret) and then landing on the 12th fret B. So basically I guess you could say the solo is in D mixolydian.

"Things ain't simple"

This one's for Kent by request, so I hope I am not way off now! :D 

Please DO correct me if I am! :)

It's in Eb. 

Intro is Eb, strumming a boogie shuffle a bit like this:

D:-------------13---------- 

A:-13-13-15-13-13-13-15-13-

E:-11-11-13-11----11-13-11-

The main part:

[Eb]It's so [Bb]sad to say
[Ab]Talking about [Eb]yesterday
[Ab]All those [Bb]good times are [Eb]gone[Bb]

The bridge: 

[C][C]We took love [Bb]easy 
[Ab]One day at a [Eb]time