Frankincense

Frankincense is a 'driver.' When used with other EOs it helps make those EOs stronger. It 'drives' those EOs in deeper into your senses [skin or inhalation.] 

Mind:

Anti-anxiety, Anti-depressant, Relaxant, Concentration

Body:
Headaches, Migraines, Sore Muscles, Muscle Spasms,

Skin and Hair:Rejuvenates Skin

Health:
Colds, Flu, Coughs, Congestion, Antiseptic, Allergies, 

Scents:
Because of the expense, I have not played with creating a diffuser scent with Frankincense.  

Links (sources):

BBC News: Frankincense: Could it be a cure for cancer? Appalachian Valley Natural Products Spark Naturals

Lemon Basil

Mind:
Alertness, Anti-anxiety, Anti-depressive 

Health:
Congestion, 

Scents:
Rosemary, Pine, or Bergamot, among others

Related:
See Sweet Basil

Links (sources):
Appalachian Valley Natural Products

Warning:

{Some sources recommend avoid or highly diluting any Basil when pregnant or nursing.} 

Lavender

Mind:
Relaxing, Calming, Antidepressant, Insomnia

Aches and Pains:
Headaches, Sore Muscles, Muscle Spasms, Arthritis

Skin and Hair:
Dry Skin, Chapped Skin or Lips, Sunburn, Minor Burns, Eczema, Dandruff 

Health:
Colds, Flu, Coughs, Antiseptic, Allergies, Cold Sores 

Digestion: 
Nausea, Motion Sickness

Scents:
Pairs well with almost everything!

Pets:
Calming

Links (sources):
Spark Naturals
Appalachian Valley Natural Products

Warning:
Although some think of Lavender (and Melaleuca) as estrogenic; it is not. Read more here.