Mix lithium with water and you get a highly energetic reaction:
2 Li (s) + 2 H2O (l) → 2 LiOH (aq) + H2 (g)
Take lithium hydroxide (LiOH) and mix it with tallow (animal fat) and you get lithium stearate (LiC18H35O2), a component of grease (ever greased wheel bearings?).
Lithium hydroxide is also useful in spacecraft, submarines, and scuba rebreathers where it helps scrub carbon dioxide (CO2) from exhaled air.
2LiOH + CO2 → Li2CO3 + H2O
Lithium carbonate is also used as a medication. It turns out that that it acts as a mood stabilizer in bipolar disorders. It's not well-understood why it works (but certainly shows how chemistry affects our moods). In 1929, lithium citrate (Li3C6H5O7), also used as a mood stabilizer, was placed into a soda originally called "lithiated lemon-lime soda." Today we know it as 7-Up (no lithium in it anymore!).
A huge use of lithium is for batteries. Most lithium batteries use lithium for the anode (negative end) and manganese dioxide (MnO2) for the cathode (positive end) of the battery. Lithium batteries are used in applications that require relatively low current (but can deliver high current pulses) and a long-life. In other words, a lot of consumer electronics.
I've read that lithium scavenged from old batteries can be used in the production of methamphetamine. This has led to completely ridiculous restrictions (like those for Sudafed) in some localities restricting the amount of batteries you can purchase at one time.
Lithium, being so reactive, is never found as a metal by itself naturally, it's mined from ore minerals like spodumene - LiAl(SiO3)2 - a proxene group mineral. Spodumene forms in lithium-rich granite pegmatites - igneous rocks which form from cooling magma at depth and grow relatively large crystals due to the presence of water and other volatiles dissolved in the molten rock.
Single crystals of spodumene as long as 50 feet have been reported from the famous, but now defunct, Etta Mine in the Black Hills of South Dakota. Below is a cross-section of the mine showing the spodumene crystals in the central ore body, an historic photo of a 47 meter long spodumene "log" excavated in 1904, and a photo I took of a tunnel at the Etta Mine a few years ago.