I downloaded a lot of Windows updates in the automatic mode.
Are they all necessary?
Can I remove some of them?
How do we know which ones are necessary?
Different kinds of updates
Internet Explorer and Windows Media Player
Also if you think you don't use Internet Explorer or Windows Media Center, you actually will do. Lots of software (both Microsoft and third party) use these programs behind the scenes. Some examples include Windows Update itself and system help, Outlook, ...
Doesn't fix any security holes directly or fixes glitches itself, but is mandatory for some upgrades to Internet Explorer, Windows Media Player and further optional updates. If you've got a legal windows license, why bothering and not install it? Doesn't hurt. If it's illegal, go out and buy a license anyhow or use some free OS.
By default, Windows only updates itself. Office (and some other software) is important, too! It is really important to opt-in for "Microsoft Update" to receive updates for these products, too. By the way, when reinstalling windows, before installing all the drivers have a look here - if you activate it, a growing amount of drivers can be installed without any hassles (internet connection required, of course).
Again - security updates are mandatory! Often third party companies don't distuingish between security and other fixes. If you've got lots of software installed, updating them can get quiet disturbing as you have to click some buttons each time (unlike Windows/Microsoft Update which runs without interaction). I recommend some free software called Ninite. You can select a set of free (some shareware) tools and get a single installer, which downloads and installs all of them without further interaction. If some software is already installed, but outdated, it will upgrade it - so keep it and if some update requests pop up, just run the utility.
If you really don't need some software, don't wait to uninstall it (if you know exactly what it is and why it is installed). Software not installed cannot do any damage. Don't remove a program if you're not totally sure, it could be some device driver or system software!
Updates & Upgrades
As there tends to be some confusion, a short distinguish between these two terms.
After some time, a software product will not get supported any more. For example, the "extended support" (the phase in which Microsoft offers security patches) of Windows XP will end in April 2014. This means, you will not receive any updates any more: If new security problems are found (and they will), there will be nobody to protect you from malware exploiting them. You antivirus software won't do, either, read below. You will need to do a (paid) upgrade to furthermore receive updates.
But I haven't got any important stuff on your computer!
(and other misconceptions)
I can't tell about the importance of your stuff. Anyhow, do you like spam? Do you like formatting your computer because of strange problems? Loved these "your computer will be shut down in 60 seconds" boxes sasser brought you some years ago?
Installing updates is a very easy way securing your computer. If it gets infected, it will send spam mails, disturb you or even steal your banking account. It will infect other computers, probably of guys who don't even aware about malware. You do, and you've got some responsibility. Or get serious problems with police if it starts sharing child porn.
These damn updates eat my precious storage
Windows keeps backups of installed updates so you can uninstall them in case of problems. Sometimes (that's really rare!) an updates wil not get installed correctly or break your system, so you can uninstall it, fix the problem and try again.
After some time you can be sure this update didn't lead to any problems. Now you can remove these backup files to get some storage back.
Under Windows XP the "Genuine Advantage" updates can be skipped. They provide no benefit (edit: see below comments).
If you are using Windows XP, and you're manually using "Microsoft Updates" instead of "Windows Updates", some of the software that is being updated isn't essential system software, including Windows Search, Windows Live, and Bing Bar. However, rather than skip updates of that software, if you don't use those programs you should uninstall them, and then don't include them in Windows Update.
In Windows Vista/7, I would NOT install optional language packs (35 or something there are now?) that you don't use/need.
Absolutely though you should always include all Office updates even for products you don't use, for similar reasons to Internet Explorer updates @Ranon talks about.
However, I wouldn't bother uninstalling any updates. If you are low on disk space you should consider other avenues first.
The question asks which Windows updates are necessary (to install), and the answer by @JensErat is very thorough at addressing that. The question has another facet that is important to address also. In some cases, the "if" isn't clear cut, and even if it is clear cut, updating can be problematic. Part of the "if" should be "when" to install and "when" to uninstall.
The first step is reading the detailed description of each update. Some decisions are clear cut:
Then there is a grey area. Microsoft has updates for components of families of software. For example, something is labelled as a fix for one program that is part of MS Office and you don't have that program loaded, but you use other of the Office programs. The descriptions often aren't comprehensive and sometimes a fix for one program in a suite will have implications for others.
Aside from that, updates aren't always benign. Sometimes they create problems that weren't there before. Earlier this year, Microsoft issued a massive collection of updates for Windows 7. Shortly thereafter, they issued another collection of updates to fix problems caused by the previous set. This is particularly a problem with Windows 7, which is approaching end-of-life and at this point, it is heavily patched. My own experience was that the old version of MS Outlook I was using became essentially incompatible with Win 7.
Most updates can be rolled back, if necessary. Some cannot. I offer these recommendations for non-security updates that you contemplate installing: