When is it recommended to use Git rebase vs. Git merge?
Do I still need to merge after a successful rebase?
TLDR: It depends on what is most important - a tidy history or a true representation of the sequence of development
If a tidy history is the most important, then you would rebase first and then merge your changes, so it is clear exactly what the new code is. If you have already pushed your branch, don't rebase unless you can deal with the consequences.
If true representation of sequence is the most important, you would merge without rebasing.
Merge means: Create a single new commit that merges my changes into the destination. Note: This new commit will have two parents - the latest commit from your string of commits and the latest commit of the other branch you're merging.
Rebase means: Create a whole new series of commits, using my current set of commits as hints. In other words, calculate what my changes would have looked like if I had started making them from the point I'm rebasing on to. After the rebase, therefore, you might need to re-test your changes and during the rebase, you would possibly have a few conflicts.
Given this, why would you rebase? Just to keep the development history clear. Let's say you're working on feature X and when you're done, you merge your changes in. The destination will now have a single commit that would say something along the lines of "Added feature X". Now, instead of merging, if you rebased and then merged, the destination development history would contain all the individual commits in a single logical progression. This makes reviewing changes later on much easier. Imagine how hard you'd find it to review the development history if 50 developers were merging various features all the time.
That said, if you have already pushed the branch you're working on upstream, you should not rebase, but merge instead. For branches that have not been pushed upstream, rebase, test and merge.
Another time you might want to rebase is when you want to get rid of commits from your branch before pushing upstream. For example: Commits that introduce some debugging code early on and other commits further on that clean that code up. The only way to do this is by performing an interactive rebase: git rebase -i
UPDATE: You also want to use rebase when you're using Git to interface to a version control system that doesn't support non-linear history (Subversion for example). When using the git-svn bridge, it is very important that the changes you merge back into Subversion are a sequential list of changes on top of the most recent changes in trunk. There are only two ways to do that: (1) Manually re-create the changes and (2) Using the rebase command, which is a lot faster.
UPDATE 2: One additional way to think of a rebase is that it enables a sort of mapping from your development style to the style accepted in the repository you're committing to. Let's say you like to commit in small, tiny chunks. You have one commit to fix a typo, one commit to get rid of unused code and so on. By the time you've finished what you need to do, you have a long series of commits. Now let's say the repository you're committing to encourages large commits, so for the work you're doing, one would expect one or maybe two commits. How do you take your string of commits and compress them to what is expected? You would use an interactive rebase and squash your tiny commits into fewer larger chunks. The same is true if the reverse was needed - if your style was a few large commits, but the repository demanded long strings of small commits. You would use a rebase to do that as well. If you had merged instead, you have now grafted your commit style onto the main repository. If there are a lot of developers, you can imagine how hard it would be to follow a history with several different commit styles after some time.
UPDATE 3: Does one still need to merge after a successful rebase?
Yes, you do. The reason is that a rebase essentially involves a "shifting" of commits. As I've said above, these commits are calculated, but if you had 14 commits from the point of branching, then assuming nothing goes wrong with your rebase, you will be 14 commits ahead (of the point you're rebasing onto) after the rebase is done. You had a branch before a rebase. You will have a branch of the same length after. You still need to merge before you publish your changes. In other words, rebase as many times as you want (again, only if you have not pushed your changes upstream). Merge only after you rebase.