While many blaim Magento for being slow, it is possible to make the Magento e-commerce application lightning fast. This requires first of all funding, because you will need to add sufficient system resources (CPU, memory) to Magento to make it run properly. But it also requires time and knowledge. For the last part - knowledge - this list helps you further.
Enable Magento cachingThis is of course the first step in optimization: Enable all the available caches in the Magento Admin Panel.
Compress imagesMany people forget that images (PNG, JPG) can be compressed, which lowers the bandwidth between the browser and the webserver. Not only the images used by the Magento skin need optimizing, but catalog images as well. Various tools allow you to compress batches of images, for instance the online tool Smush.It.
Disable unneeded Magento modulesBy disabling Magento modules that you do not need, less resources are needed - as simple as that. Modules could be disabled through the configuration in the Magento Admin Panel, or by editing XML-files in app/etc/modules. For instance, disable Mage_Log which performs queries on every request, but is not needed if you gather site statistics using external programs.
Enable flat catalogs for smaller webshopsFor smaller webshops switching from the complex EAV-structure to a flat catalog could save time. This optimization is dubious and depends on many parameters, so do not take this step lightly.
W3C complianceWhile it could be argued that this is less important with the coming of HTML5, it is still a fact that if your webpages are filled with ugly errors, the browser will have a harder time interpreting it. If you stick to W3C compliance, it is made sure the browser engine has an easy job parsing your HTML-code.
Configure PHP optionsMost PHP settings actually do not influence the performance of Magento, but just set certain limits. For instance, settings like memory_limit and max_execution_time do not increase the page load but just make sure that certain actions do not timeout or run into memory problems.
Session storageWith Magento, sessions could be stored in files or in the database (by configuring app/etc/local.xml). Which option performs best, really depends on how the hosting environment is setup. If MySQL databases perform well, session storage in the database could benefit your site. But if MySQL is not setup correctly, the best choice might be files.
Use a PHP acceleratorBy opcode caching, PHP-execution could be fastened. There are various PHP accelerators doing this job (APC, ZendOptimizer+, eAccelerator, XCache). Both APC and ZendOptimizer+ are working flawless with Magento.
Tune PHP realpath_cacheBy tuning the PHP realpath_cache_size to for instance 128K (default is 16K) and the realpath_cache_ttl to 86400, things might be speeding up. Make sure you don't run out of memory, because every Apache child will consume the configured caching size.
Beware 404 errorsEvery time a file (like a stylesheet or image) is not found, this generates a 404 error. Because the default 404 of Magento is caught by the application of Magento itself, this causes the Magento application to start for every 404 encountered. Check your Apache logs to make sure all 404 errors are solved.
Disable Magento loggingWithin the Magento configuration, you can enable logging under the Developers-tab. Depending on the Magento modules this could lead to more logs needed to be written to the filesystem, slowing down your shop. Because the logging-abilities are only needed to debug something, in daily usage, it's best to disable logging altogether.
MySQL table optimizationThrough phpMyAdmin, you can perform the command OPTIMIZE TABLE on specific Magento database-tables. When a table is cluttered, this could lead to improved performance. This does not only count for the complex EAV-tables, but also for regular MySQL tables that are used frequently (for instance, core_config_data).
Besides merging, crunching is also an option offered by FooMan Speedster: It removes whitespaces from the output, but when compression is already applied to CSS, this option is less needed.
Use Magento Compiler module
The Magento Compiler module limits the number of directories that PHP has to search through when looking for PHP-files. This decreases the PHP execution-time, which speeds up the Magento application in general.
Be warned that you need to be careful when making changes to your Magento system, while the Magento Compiler is enabled. Upgrades should only be undertaken when the compiler is (temporarily) disabled.
One very neat trick that speeds up things tremenduously is to create a tmpfs-mount specifically for the includes/src folder. Note that this tmpfs-mount needs to be at least 100Mb - preferably 200Mb.