Yes,

Like del piero says, the gravitational field of each one affects the shape of the other, so it's similar to the "metaballs" used in computer graphics.

The exact shape will depend on the geometry, but it usually looks like two fingers reaching out to meet, like in Michelangelo's "The Creation of Adam". You can really see it in the first & last videos here, but there are some good videos of death spirals in between.

Note that the pulsing at the end of the first video isn't anything real; it's caused by the change in magnitude of the color scale shown in the bottom right corner.

There are also a couple of decent still frames (head on collisions of equally massed holes) on these two pages:

http://www.psc.edu/science/winicour.html
http://www.psc.edu/research/graphics/gallery/winicour.php. 

This one has a shot of asymetrically massed black holes, just after they join (with the original event horizons drawn underneath):

http://physics.aps.org/story/v25/st22

Sorry about the links I don't have enough points to post more than two real ones.

Yes,

Like del piero says, the gravitational field of each one affects the shape of the other, so it's similar to the "metaballs" used in computer graphics.

The exact shape will depend on the geometry, but it usually looks like two fingers reaching out to meet, like in Michelangelo's "The Creation of Adam". You can really see it in the first & last videos here, but there are some good videos of death spirals in between.

Note that the pulsing at the end of the first video isn't anything real; it's caused by the change in magnitude of the color scale shown in the bottom right corner.

There are also a couple of decent still frames (head on collisions of equally massed holes) on these two pages: 1,2.

This one has a shot of asymmetrically massed black holes, just after they join (with the original event horizons drawn underneath):