Computer Hope

If you're looking for tools to see how fast your system really is - either for diagnostics purposes, deciding what to upgrade next, or just for bragging rights - look no further!  I've separated these out into categories and will update this as time permits, I hope you find the information useful!  If you have any queries about anything in this FAQ, whether related to the specific tools or not, please create a new thread in the appropriate section - probably Hardware - and we'll assist.  I'm also happy to take feedback on this thread via PM, if you know of a useful tool that isn't here or spot an error.

General system performance

PCMark - one of the oldest and most well-known general benchmarking tools, PCMark by Futuremark is now on version 8.  There's a free version available to download from their website, or there are several paid options.  The usual paid option is known as "Advanced Edition" and is available to buy on Steam rather than from Futuremark's website - the "Professional Edition" is really for benchmarking websites or large organisations, it's very expensive at just under $1500 and is basically overkill for any home user.  The differences between the free Basic version and the paid Advanced version are detailed at the bottom of the main page linked above, but essentially the paid version gives you access to 5 test suites instead of 3 (the additional two test suites are storage which is very useful, and applications which uses MS Office and Adobe Creative Suite if you have it installed), lets you run the battery life test, lets you run individual tests from each suite, gives you some pretty graphs to look at, and finally lets you save your results offline.  PCMark is fairly real-world in its testing as it uses actual applications such as LibreOffice and a web browser to test performance doing a set of scripted tasks such as loading web pages and creating documents.  There are some basic 3D tests in there as well, nothing overly demanding.  Overall it's a good test suite IMO, with the main downsides being that one of the most useful tests is not free, the long run-time for each suite of tests (expect 20 minutes for the shortest), and the hefty download size - it's nearly 3GB.

3D performance/gaming

3DMark - also by Futuremark, this is probably the most well-known synthetic 3D benchmark suite.  There's a free version available to download from the website, or again as with PCMark there's a "Professional Edition" aimed mainly at reviewers, and an "Advanced Edition" available to buy on Steam or from Futuremark's website which gives you graphs, some more tests, much more customizability on each available suite, and the ability to loop the benchmarks for stability testing.

Unigine Heaven - this is a few years old but still relevant today as it uses DX11's tesselation features to really push your graphics card's performance on higher settings.  There are several ways to run the Heaven benchmark - it can either continuously run, showing your FPS and other stats, or there's a benchmark mode to give you a score for your system.  The free version does both of these modes and also lets you customize the settings, e.g. the detail, resolution and how much tesselation to use - whereas the paid Advanced version includes the ability to loop the benchmark mode, automate Heaven from the command line and produce reports in CSV format.  There's also a Pro edition which is unnecessary for most users.  Heaven is useful as a stress-testing tool if you suspect your graphics card may have an issue, as well as for comparing benchmark results against similar cards to make sure your card is performing properly.

Unigine Valley - from the same company as Heaven, Valley is a newer benchmark which isn't focussed on tesselation, instead it's set outside so you have volumetric lighting, ambient occlusion, dynamic weather, and procedural object placement.  The Basic/Advanced/Pro editions are the same as Heaven in terms of what features they give you, so for most uses the Basic version gives you everything you need as you can run the test continuously or perform benchmark runs.

CPU/RAM

I've grouped CPU and RAM benchmarks together because often the performance of one will affect results from the other.

Asus/ROG Realbench - this does have an element of GPU performance too, but it's mainly CPU and RAM-bound.  Realbench uses open source applications bundled with the benchmark to give you real-world performance result.  The benchmark generally takes around 15 minutes to run, and will stop if you move the mouse or press a button on the keyboard whilst it's running, this is to prevent alterations or tinkering.  It's 100% free and you can loop the benchmark to use as a stability test.  The leaderboard section lets you compare your scores to others, the only slight issue is that by ROG's nature, most results are from fairly high-end systems, so sometimes it's difficult to find a system that compares to yours unless you too have a recent-ish high-end system.  Realbench is also 64-bit only, because...well, from their FAQ "We made the conscious choice to focus on a 64-bit version only. We believe everyone should be running a 64-bit OS these days considering modern GPU/DDR3 memory capacities. Equally, we've not tested it on antiquated XP-64, and since less than 1% of our site visitors use Vista, we've solely focused on Win 7 and Win 8/8.1."

Superpi - a very simple, single-threaded benchmark that just calculates Pi to the number of digits specified.  It's useless for comparing multi-core performance, obviously, and not that great for most stability testing, but it can be a useful tool nontheless.

Y-Cruncher - this is a multi-threaded tool which can be used for benchmarking and/or stress testing.  It calculates Pi and other constants, some of the larger calculations will require a lot of RAM and therefore there's even a "swap mode" to enable usage of one or several storage devices as swap space.  Thanks to DaveLembke for the recommendation.

wPrime - another simple tool which calculates square roots.  This is multithreaded so it can be a good indicator of raw CPU/RAM performance as well as a simple stability test.

MaxxMem2 - this is a very small and simple memory benchmark which gives you scores for copy, read, write, and latency.  I sometimes get an error on launching this, not sure if it's because I have more RAM than it's expecting, or that I'm on Windows 10 which isn't officially supported, but it works fine the second time I launch it - worth mentioning in case anyone else runs into this.

MaxxMem2 Multi - very similar to the above but it seems to use multiple channels.

AIDA64 - formerly Lavalys Everest, this is a shareware product that gives you a whole lot of information about your PC - specs, hardware monitoring, sofwtare and so forth - but also has a great benchmark utility under Tools - Cache and Memory Benchmark.  Some readings aren't available in the trial version but it's still a very useful benchmark.

Storage

CrystalDiskMark - one of my favourite disk benchmarks, before I go on I'll strongly advise downloading the portable edition (zip) and extracting the files to run from there - the full installer version has at some points contained other programs bundled with it, this isn't true for all versions but the portable edition avoids any risk of this.  CrystalDiskMark is a good test for any kind of storage, whether it's a HDD, SSD, SSHD, or even a flash drive.  There are options to run each test 1-9 times, with data of 50MB-32GB - the default option of 5 passes with 1GB of data should be fine for most uses, but if you're benchmarking slower flash drives or HDDs you may want to reduce this to say, 3 x 500MB, as the test won't take as long.

ATTO - often used by manufacturers along with IOMeter to get their advertised read/write speeds, I've linked to Techpowerup! rather than the ATTO website because I can't actually get a download link from there.  Techpowerup is a safe site to get this from at the time of writing (I download tools from there regularly) but as always please exercise caution as it's not direct from the developer's website.  ATTO's interface isn't the prettiest as it's quite an old tool, but the results are still very useful.

Anvil Storage Utilities - anoither great benchmark especially for SSDs, unfortunately there's no manufacturer's download link and a lot of versions across the web have expiry dates and/or are older versions.  As above, please exercise caution when downloading, I trust Gugu3D to be a reputable provider but I can't guarantee this.

AS-SSD - another great utility, the website is in German and you may have to change the language when you open AS-SSD for the first time. Download link is right at the bottom of the linked page.

HD Tune - this is basically just for HDDs, I would not recommend running this on an SSD.  HD Tune pro is paid software and still being developed, however the older 2.55 version is free on their download page.  There's a benchmark with a graph (very useful for diagnostics too, if you see a very spiky graph it's usually an indicator that soemthing's wrong) and an error scanner too, to check for bad sectors.  HD Tune also displays SMART info which can be useful for diagnostics.