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.
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.
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.
There are various Full Page Cache (FPC) solutions out there, in the form of extensions (LestiFPC, Enterprise Edition) or complete solutions (Nginx, Varnish). In all cases, FPC should not have the first focus. When your Magento shop is slow, it's because of certain reasons, and those reasons need to be investigated. When your catalog pages are fast (thanks to FPC) but your dynamic pages are still slow, the goal of having a speedy site - to attract more customers, thus more revenue - is lost. So in general, FPC should be implemented to make the site lightning fast, while the site without FPC is already fast enough.
One strategy for tuning is to tune everything to the max, literally everything. This means that you are tweaking for maximum performance and squeezing every millisecond out of all your components. However, you will also need the budget for that. Another strategy is to tune exactly that thing that requires tuning. This is more efficient, but requires you to know which tuning would have the most impact.
The big question of which tuning should be done first, can not be answered without custom advice. Normally, a Magento performance expert would need to go in and check the entire shop before such a solid advice would come. We have bundled all the neat tricks on this and have developed a semi-automated advice mechanism - dubbed Magento Performance Insights - that allows you to summarize the entire environent (Magento, PHP, MySQL) quickly and come up with clever adjustments. For instance, some settings can be tuned straight-forward, other tuning relies on the size of your catalog, the number of Store Views, etcetera. Our Performance Insights service allows you to get a complete list of what can be done, custom-made for your specific Magento shop, in a complete report - useful for any third party developer. More information is available here.