I have a 50 foot run from my breaker panel to my garage where I will put a junction box to distribute the power to a light, 2 outlets and a garage door opener.

Currently there is a wire already suspended from the mast head to the garage, and I plan on hanging my wire from that.

I know there will be a voltage drop but I'm not sure how much. It's going to be on a 20 amp break so I was thinking a #10 UF would prevent voltage drop for that kind of distance. What do you guys/girls think?

I think for 50' it is not worth worrying about.
#12 is fine.

Calculating Voltage Drop - 1 Phase

I (Amperage - also known as Current)

VD (Voltage Drop)

R (Resistivity of wire - taken from NEC Chapter 9 Table 8 (http://www.scribd.com/doc/29572773/NEC-Chapter-9-Tables-and-Annexes-B-and-C))

L (Length of run - we typically calculate the drop per 1000 ft lengths)

CM (Circular Mils of Wire (http://infohost.nmt.edu/~armiller/homerepair/conduitsize.htm)- measure of the diameter (thickness) of the wire - again available from NEC tables)

K (Resistivity Constant - 12 for Copper, 18 for Aluminum)

Source: Electrician-ElectricalContractor.com (http://www.electrician-electricalcontractor.com/calculatevoltagedrop.html)

Thanks, that makes my wallet happy.

Not really, you cannot use type "UF"(Underground Feeder)for an above ground run if is not listed for that usage. If it is, you should see, "Sun light Ristance" or similar words on the cable sheath.

Once again Don is correct.

What kind should I use?

UF cable is rated sunlight resistant.