The following is my short list of components and modules that I have used in almost all my Joomla site development. Not all of the components or modules are free, but all of them do work. After spending countless hours fixing marginal and buggy code in various Joomla plugins, components, and modules; I have developed a shortlist of components that require very little if any "fixes". So without further ado, here are my Top 5:
1. Chronoforms: Absolutely perfect for developing any type of form for your website. Chronforms includes client side validation for any of your fields or you may also use your own scripting for validation. You can customize your forms using your own styling and depending on how savvy you are with PHP you can provide your own server side validation and form processing for a database. The component is free, but has a link that will appear unless you pay for an entitlement. Currently the price for entitlements ranges from $25.00 on up. Additionally the forum support is one of the best. Check out an example Chronoform here.
2. Akeeba Backup: Best backup system for Joomla. Akeeba was formerly called Joomla Pack. This component allows you to fully backup your site in a proprietary archive format thus creating a full re-install package. The reinstallation package allows you to install your site anywhere, even to a new domain. Akeeba backup also offers a number of tools inclusive of cron jobs, so that you never even have to press a button after set up to have a fully backed up site. Also did I mention it is free.
3.Module Place Here: The features and customizations for this module are endless. The module allows you to show categories, sections, and articles in a variety of ways. I like to use this module when I need a list of articles a certain way. There are modules and parts of Joomla that can offer some of the functionality, but not all in one module.
4.JCE- Editor: I have tried other editors, notably Joomla JCK, because I felt that JCE was a little heavy, but I always end up deploying JCE for most of my clients. The editor plays nicely with most plugins and doesn't destroy the backend styling of other components like some other editors. Additionally JCE has plugins for adding files, video, uploading images from within the current article you are editing and more. You may also customize the editor for the various groups in Joomla, which is very nice for sites that have multiple people adding content.
5.RokStories:Slideshow: My favorite slideshow module. This slideshow module allows you to show content with your slides, pictures only, control the slide intervals, and whether the slide show starts automatically. Basically I have had very few problems customizing this module for various templates.