gitignore all files of extension in directory

It would appear that the ** syntax is supported by git as of version 1.8.2.1 according to the documentation.

Two consecutive asterisks (“**“) in patterns matched against full pathname may have special meaning:

• A leading “**” followed by a slash means match in all directories. For
  example, “**/foo” matches file or directory “foo” anywhere, the same
  as pattern “foo“. “**/foo/bar” matches file or directory “bar”
  anywhere that is directly under directory “foo“.

• A trailing “/**” matches everything inside. For example, “abc/**”
  matches all files inside directory “abc“, relative to the location of
  the .gitignore file, with infinite depth.

• A slash followed by two consecutive asterisks then a slash matches
  zero or more directories. For example, “a/**/b” matches “a/b“,
  “a/x/b“, “a/x/y/b” and so on.

• Other consecutive asterisks are considered invalid.