For those wondering why it works (as I was at first):

You want to go back to C, and move D and E to the new branch. Here's what it looks like at first:

A-B-C-D-E (HEAD)
        ↑
      master

After git branch newBranch:

    newBranch
        ↓
A-B-C-D-E (HEAD)
        ↑
      master

After git reset --hard HEAD~2:

    newBranch
        ↓
A-B-C-D-E (HEAD)
    ↑
  master

Since a branch is just a pointer, master pointed to the last commit. When you made newBranch, you simply made a new pointer to the last commit. Then using git reset you moved the master pointer back two commits. But since you didn't move newBranch, it still points to the commit it originally did.

In General...

The method exposed by sykora is the best option in this case. But sometimes is not the easiest and it's not a general method. For a general method use git cherry-pick:

To achieve what OP wants, its a 2-step process:

Step 1 - Note which commits from master you want on a newbranch

Execute

git checkout master
git log

Note the hashes of (say 3) commits you want on newbranch. Here I shall use:
C commit: 9aa1233
D commit: 453ac3d
E commit: 612ecb3

Note: You can use the first seven characters or the whole commit hash

Step 2 - Put them on the newbranch

git checkout newbranch
git cherry-pick 612ecb3
git cherry-pick 453ac3d
git cherry-pick 9aa1233

OR (on Git 1.7.2+, use ranges)

git checkout newbranch
git cherry-pick 612ecb3..9aa1233

git cherry-pick applies those three commits to newbranch.

Yet another way to do this, using just 2 commands. Also keeps your current working tree intact.

git checkout -b newbranch # switch to a new branch
git push . +HEAD~3:master # make master point to some older commit 

Being able to push to . is a nice trick to know.

Late Edit: Now that I know about git branch -f the right way to do it is:

git checkout -b newbranch # switch to a new branch
git branch -f master HEAD~3 # make master point to some older commit 

Which is the same, but less "magic"

Most previous answers are dangerously wrong!

Do NOT do this:

git branch -t newbranch
git reset --hard HEAD~3
git checkout newbranch

As the next time you run git rebase (or git pull --rebase) those 3 commits would be silently discarded from newbranch! (see explanation below)

Instead do this:

git reset --keep HEAD~3
git checkout -t -b newbranch
git cherry-pick ..HEAD@{2}

• First it discards the 3 most recent commits (--keep is like --hard, but safer, as fails rather than throw away uncommitted changes).
• Then it forks off newbranch.
• Then it cherry-picks those 3 commits back onto newbranch. Since they're no longer referenced by a branch, it does that by using git's reflog: HEAD@{2} is the commit that HEAD used to refer to 2 operations ago, i.e. before we 1. checked out newbranch and 2. used git reset to discard the 3 commits.

Warning: the reflog is enabled by default, but if you've manually disabled it (e.g. by using a "bare" git repository), you won't be able to get the 3 commits back after running git reset --keep HEAD~3.

An alternative that doesn't rely on the reflog is:

# newbranch will omit the 3 most recent commits.
git checkout -b newbranch HEAD~3
git branch --set-upstream-to=oldbranch
# Cherry-picks the extra commits from oldbranch.
git cherry-pick ..oldbranch
# Discards the 3 most recent commits from oldbranch.
git branch --force oldbranch oldbranch~3

(if you prefer you can write @{-1} - the previously checked out branch - instead of oldbranch).

Technical explanation

Why would git rebase discard the 3 commits after the first example? It's because git rebase with no arguments enables the --fork-point option by default, which uses the local reflog to try to be robust against the upstream branch being force-pushed.

Suppose you branched off origin/master when it contained commits M1, M2, M3, then made three commits yourself:

M1--M2--M3  <-- origin/master
         \
          T1--T2--T3  <-- topic

but then someone rewrites history by force-pushing origin/master to remove M2:

M1--M3'  <-- origin/master
 \
  M2--M3--T1--T2--T3  <-- topic

Using your local reflog, git rebase can see that you forked from an earlier incarnation of the origin/master branch, and hence that the M2 and M3 commits are not really part of your topic branch. Hence it reasonably assumes that since M2 was removed from the upstream branch, you no longer want it in your topic branch either once the topic branch is rebased:

M1--M3'  <-- origin/master
     \
      T1'--T2'--T3'  <-- topic (rebased)

This behavior makes sense, and is generally the right thing to do when rebasing.

So the reason that the following commands fail:

git branch -t newbranch
git reset --hard HEAD~3
git checkout newbranch

is because they leave the reflog in the wrong state. Git sees newbranch as having forked off the upstream branch at a revision that includes the 3 commits, then the reset --hard rewrites the upstream's history to remove the commits, and so next time you run git rebase it discards them like any other commit that has been removed from the upstream.

But in this particular case we want those 3 commits to be considered as part of the topic branch. To achieve that, we need to fork off the upstream at the earlier revision that doesn't include the 3 commits. That's what my suggested solutions do, hence they both leave the reflog in the correct state.

For more details, see the definition of --fork-point in the git rebase and git merge-base docs.

This doesn't "move" them in the technical sense but it has the same effect:

A--B--C  (branch-foo)
 \    ^-- I wanted them here!
  \
   D--E--F--G  (branch-bar)
      ^--^--^-- Opps wrong branch!

While on branch-bar:
$ git reset --hard D # remember the SHAs for E, F, G (or E and G for a range)

A--B--C  (branch-foo)
 \
  \
   D-(E--F--G) detached
   ^-- (branch-bar)

Switch to branch-foo
$ git cherry-pick E..G

A--B--C--E'--F'--G' (branch-foo)
 \   E--F--G detached (This can be ignored)
  \ /
   D--H--I (branch-bar)

Now you won't need to worry about the detached branch because it is basically
like they are in the trash can waiting for the day it gets garbage collected.
Eventually some time in the far future it will look like:

A--B--C--E'--F'--G'--L--M--N--... (branch-foo)
 \
  \
   D--H--I--J--K--.... (branch-bar)

Had just this situation:

Branch one: A B C D E F     J   L M  
                       \ (Merge)
Branch two:             G I   K     N

I performed:

git branch newbranch 
git reset --hard HEAD~8 
git checkout newbranch

I expected that commit I would be the HEAD, but commit L is it now...

To be sure to land on the right spot in the history its easier to work with the hash of the commit

git branch newbranch 
git reset --hard #########
git checkout newbranch

To do this without rewriting history (i.e. if you've already pushed the commits):

git checkout master
git revert <commitID(s)>
git checkout -b new-branch
git cherry-pick <commitID(s)>

Both branches can then be pushed without force!