I'd like to know how much weight a 4X6, 4X8, and 4X10 wood beam can carry over a 15 foot span. The weight would be evenly distributed.

Glulam?
Microlam?
LVL?
Fir?
Spruce?
Pine?
Box beam

Lot's of kinds of wood in this world - all with different peculiarities.

i am planning to use a standard douglas fir beam(solid) that is available from Home Depot.

Engineering advice from an internet site like this with no other information about the design of the house is worth what you pay for it.

A fifteen foot sapn is likely to require a man-made LVL or glulam. You give no details about what it will support. Roof only?
or just taking the bounce out of some floor joists midspan with no actaul loading?
header for three stories above?

Complete plans are necessary for complete answer but a generic rule of themb would call for this beam in fir to be a 4 x 18 or 4 x 16