How to clone git repository with specific revision/changeset?

UPDATE 2 Since Git 2.5.0 the feature described below can be enabled on server side with configuration variable uploadpack.allowReachableSHA1InWant, here the GitHub feature request and the GitHub commit enabling this feature. Note that some Git servers activate this option by default, e.g. Bitbucket Server enabled it since version 5.5+. See this answer on Stackexchange for a exmple of how to activate the configuration option.

UPDATE 1 For Git versions 1.7 < v < 2.5 use git clone and git reset, as described in Vaibhav Bajpai's answer

If you don't want to fetch the full repository then you probably shouldn't be using clone. You can always just use fetch to choose the branch that you want to fetch. I'm not an hg expert so I don't know the details of -r but in git you can do something like this.

# make a new blank repository in the current directory
git init

# add a remote
git remote add origin url://to/source/repository

# fetch a commit (or branch or tag) of interest
# Note: the full history up to this commit will be retrieved unless 
#       you limit it with '--depth=...' or '--shallow-since=...'
git fetch origin <sha1-of-commit-of-interest>

# reset this repository's master branch to the commit of interest
git reset --hard FETCH_HEAD

$ git clone $URL
$ cd $PROJECT_NAME
$ git reset --hard $SHA1

To again go back to the most recent commit

$ git pull

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To save online (remote) the reverted commit, you must to push enforcing origin:

git push origin -f