There are a few modules/plugins that I always use in Joomla websites because of what they do and how reliable they have been, and because they are free. I decided to share them with you in case they might help.
This module has come in very handy quite a few times when I need to have an article inside another article. I can choose which parts show and I can even stylize the output a little bit. There is a paid version with more options but I haven’t had to purchase yet.
The contact form in Joomla is quite insufficient so I always install a contact form module to get something better. The best one I found is aiContactSafe. It is highly customizable and has a ton of features. It can be quite complicated and sometimes a little trial and error is involved to get the settings correct but I haven’t had it fail yet. Last time I looked this module had not been updated for Joomla 3.2 so be careful.
This is a very short list because I am short on time, but I will add more eventually. There are thousands of modules and plugins available, many of them are probably good, so feel free to add them to the comments. Back them up though. If I find that the module has a low rating and/or lots of complaints I may delete the comment.