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Git is not better than Subversion. But is also not worse. It's different.
The key difference is that it is decentralized. Imagine you are a developer on the road, you develop on your laptop and you want to have source control so that you can go back 3 hours.
With Subversion, you have a Problem: The SVN Repository may be in a location you can't reach (in your company, and you don't have internet at the moment), you cannot commit. If you want to make a copy of your code, you have to literally copy/paste it.
With Git, you do not have this problem. Your local copy is a repository, and you can commit to it and get all benefits of source control. When you regain connectivity to the main repository, you can commit against it.
This looks good at first, but just keep in mind the added complexity to this approach.
Git seems to be the "new, shiny, cool" thing. It's by no means bad (there is a reason Linus wrote it for the Linux Kernel development after all), but I feel that many people jump on the "Distributed Source Control" train just because it's new and is written by Linus Torvalds, without actually knowing why/if it's better.
Subversion has Problems, but so does Git, Mercurial, CVS, TFS or whatever.
Edit: So this answer is now a year old and still generates many upvotes, so I thought I'll add some more explanations. In the last year since writing this, Git has gained a lot of momentum and support, particularly since sites like GitHub really took off. I'm using both Git and Subversion nowadays and I'd like to share some personal insight.
First of all, Git can be really confusing at first when working decentralized. What is a remote? and How to properly set up the initial repository? are two questions that come up at the beginning, especially compared to SVN's simple "svnadmin create", Git's "git init" can take the parameters --bare and --shared which seems to be the "proper" way to set up a centralized repository. There are reasons for this, but it adds complexity. The documentation of the "checkout" command is very confusing to people changing over - the "proper" way seems to be "git clone", while "git checkout" seems to switch branches.
Git REALLY shines when you are decentralized. I have a server at home and a Laptop on the road, and SVN simply doesn't work well here. With SVN, I can't have local source control if I'm not connected to the repository (Yes, I know about SVK or about ways to copy the repo). With Git, that's the default mode anyway. It's an extra command though (git commit commits locally, whereas git push origin master pushes the master branch to the remote named "origin").
As said above: Git adds complexity. Two modes of creating repositories, checkout vs. clone, commit vs. push... You have to know which commands work locally and which work with "the server" (I'm assuming most people still like a central "master-repository").
Also, the tooling is still insufficient, at least on Windows. Yes, there is a Visual Studio AddIn, but I still use git bash with msysgit.
SVN has the advantage that it's MUCH simpler to learn: There is your repository, all changes to towards it, if you know how to create, commit and checkout and you're ready to go and can pickup stuff like branching, update etc. later on.
Git has the advantage that it's MUCH better suited if some developers are not always connected to the master repository. Also, it's much faster than SVN. And from what I hear, branching and merging support is a lot better (which is to be expected, as these are the core reasons it was written).
This also explains why it gains so much buzz on the Internet, as Git is perfectly suited for Open Source projects: Just Fork it, commit your changes to your own Fork, and then ask the original project maintainer to pull your changes. With Git, this just works. Really, try it on Github, it's magic.
What I also see are Git-SVN Bridges: The central repository is a Subversion repo, but developers locally work with Git and the bridge then pushes their changes to SVN.
But even with this lengthy addition, I still stand by my core message: Git is not better or worse, it's just different. If you have the need for "Offline Source Control" and the willingness to spend some extra time learning it, it's fantastic. But if you have a strictly centralized Source Control and/or are struggling to introduce Source Control in the first place because your co-workers are not interested, then the simplicity and excellent tooling (at least on Windows) of SVN shine.
With Git, you can do practically anything offline, because everybody has their own repository.
Making branches and merging between branches is really easy.
Even if you don't have commit rights for a project, you can still have your own repository online, and publish "push requests" for your patches. Everybody who likes your patches can pull them into their project, including the official maintainers.
It's trivial to fork a project, modify it, and still keep merging in the bugfixes from the HEAD branch.
Git works for the Linux kernel developers. That means it is really fast (it has to be), and scales to thousands of contributors. Git also uses less space (up to 30 times less space for the Mozilla repository).
Git is very flexible, very TIMTOWTDI (There is more than one way to do it). You can use whatever workflow you want, and Git will support it.
Finally, there's GitHub, a great site for hosting your Git repositories.
Drawbacks of Git:
it's much harder to learn, because Git has more concepts and more commands.
revisions don't have version numbers like in subversion
many Git commands are cryptic, and error messages are very user-unfriendly
Other answers have done a good job of explaining the core features of Git (which are great). But there's also so many little ways that Git behaves better and helps keep my life more sane. Here are some of the little things:
Git has a 'clean' command. SVN desperately needs this command, considering how frequently it will dump extra files on your disk.
Git has the 'bisect' command. It's nice.
SVN creates .svn directories in every single folder (Git only creates one .git directory). Every script you write, and every grep you do, will need to be written to ignore these .svn directories. You also need an entire command ("svn export") just to get a sane copy of your files.
In SVN, each file & folder can come from a different revision or branch. At first, it sounds nice to have this freedom. But what this actually means is that there is a million different ways for your local checkout to be completely screwed up. (for example, if "svn switch" fails halfway through, or if you enter a command wrong). And the worst part is: if you ever get into a situation where some of your files are coming from one place, and some of them from another, the "svn status" will tell you that everything is normal. You'll need to do "svn info" on each file/directory to discover how weird things are. If "git status" tells you that things are normal, then you can trust that things really are normal.
You have to tell SVN whenever you move or delete something. Git will just figure it out.
Ignore semantics are easier in Git. If you ignore a pattern (such as *.pyc), it will be ignored for allsubdirectories. (But if you really want to ignore something for just one directory, you can). With SVN, it seems that there is no easy way to ignore a pattern across all subdirectories.
Another item involving ignore files. Git makes it possible to have "private" ignore settings (using the file .git/info/exclude), which won't affect anyone else.
Branches are lightweight and merging is easy, and I mean really easy.
It's distributed, basically every repository is a branch. It's much easier to develop concurrently and collaboratively than with Subversion, in my opinion. It also makes offline development possible.
It doesn't impose any workflow, as seen on the above linked website, there are many workflows possible with Git. A Subversion-style workflow is easily mimicked.
Git repositories are much smaller in file size than Subversion repositories. There's only one ".git" directory, as opposed to dozens of ".svn" repositories (note Subversion 1.7 and higher now uses a single directory like Git.)
The staging area is awesome, it allows you to see the changes you will commit, commit partial changes and do various other stuff.
Stashing is invaluable when you do "chaotic" development, or simply want to fix a bug while you're still working on something else (on a different branch).
You can rewrite history, which is great for preparing patch sets and fixing your mistakes (beforeyou publish the commits)
… and a lot more.
There are some disadvantages:
There aren't many good GUIs for it yet. It's new and Subversion has been around for a lot longer, so this is natural as there are a few interfaces in development. Some good ones include TortoiseGitand GitHub for Mac.
Partial checkouts/clones of repositories are not possible at the moment (I read that it's in development). However, there is submodule support.Git 1.7+ supports sparse checkouts.
It might be harder to learn, even though I did not find this to be the case (about a year ago). Git has recently improved its interface and is quite user friendly.
In the most simplistic usage, Subversion and Git are pretty much the same. There isn't much difference between:
svn checkout svn://foo.com/bar bar
svn commit -m "foo"
git clone email@example.com:foo/bar.git
git commit -a -m "foo"
Where Git really shines is branching and working with other people.
Well, it's distributed. Benchmarks indicate that it's considerably faster (given its distributed nature, operations like diffs and logs are all local so of course it's blazingly faster in this case), and working folders are smaller (which still blows my mind).
When you're working on subversion, or any other client/server revision control system, you essentially create working copies on your machine by checking-out revisions. This represents a snapshot in time of what the repository looks like. You update your working copy via updates, and you update the repository via commits.
With a distributed version control, you don't have a snapshot, but rather the entire codebase. Wanna do a diff with a 3 month old version? No problem, the 3 month old version is still on your computer. This doesn't only mean things are way faster, but if you're disconnected from your central server, you can still do many of the operations you're used to. In other words, you don't just have a snapshot of a given revision, but the entire codebase.
You'd think that Git would take up a bunch of space on your harddrive, but from a couple benchmarks I've seen, it actually takes less. Don't ask me how. I mean, it was built by Linus, he knows a thing or two about filesystems I guess.
You can commit broken things. It doesn't matter because other peoples won't see them until you publish. Publish time is different of commit time.
Because of this you can commit more often.
You can merge complete functionnality. This functionnality will have its own branch. All commits of this branch will be related to this functionnality. You can do it with a CVCS however with DVCS its the default.
You can search your history (find when a function changed )
You can undo a pull if someone screw up the main repository, you don't need to fix the errors. Just clear the merge.
When you need a source control in any directory do : git init . and you can commit, undoing changes, etc...
It's fast (even on Windows )
The main reason for a relatively big project is the improved communication created by the point 3. Others are nice bonuses.
Although Google Code natively speaks Subversion, you can easily use Git during development. Searching for "git svn" suggests this practice is widespread, and we too encourage you to experiment with it.
Using Git on a Svn Repository gives me benefits:
I can work distributed on several machines, commiting and pulling from and to them
I have a centralbackup/public svn repository for others to check out