What color do blue and purple make?
Blue and Purple make indigo.

Blue and Purple make indigo, #55308c. That is the result in equal parts, mixing pigment rather than light - paint, ink and dye all behave this way.
Equal parts blue and purple · #55308c
Change the ratio
Very little of a mix is ever half and half. Shifting the balance moves the result along the range between the two colours.
3 parts blue, 1 part purple · #3f4793
Equal parts · #55308c
1 part blue, 3 parts purple · #6a1886
Lighter and darker
With white added - a tint · #aa98c6
With black added - a shade · #331d54
Why it works
Pigment mixes subtractively: blue paint absorbs the wavelengths it is not reflecting, purple absorbs its own set, and indigo is what neither of them absorbed. This is why paint behaves differently from a screen, where light adds together instead.
Frequently asked questions
What color do blue and purple make?
Blue and Purple make indigo, #55308c. Mixed in equal parts that is the result you get with paint, ink or any other pigment.
How do I make the result lighter or darker?
Add white for a tint - here that gives lavender. Add black for a shade, which gives indigo. Add white a little at a time, because it takes far less than people expect to shift a mix.
What happens if I use more blue than purple?
Three parts blue to one part purple gives indigo. Reversing it to one part blue and three parts purple gives purple instead.
Does this work the same way on a screen?
No. Screens mix light additively, so red and green light make yellow there. These results are subtractive - paint, ink, dye and pigment - which is what people mean when they ask what two colours make.