SSH (secure shell) access to your web-server can be very helpful for admins. It simplifies things like troubleshooting, importing and exporting database dumps, cleaning malware affected codes and what not! However, if you are not really interested in getting your hands dirty coding on a command line interface (CLI), almost every shared web hosting will provide you with a easy to navigate control panel. (Usually cPanel)
If you are a scripting expert, having a shell access can help you automate a lot of things. However, there is the dark side of shell access on shared web servers. Many times you may have directories with read,write,execute permissions. This is what can destroy your websites by hacking activities. Another user can upload and execute sneaky scripts and create havoc!
As an alternative to direct shell access, webhosts do allow other ways of executing scripts via php and also through cronjobs.
Though most cheap shared web hosting companies do provide shell access for free (or for a small fee), most of the times the permissions are limited. Out of the top shared hosting providers, HostGator does provide shell access without any extra charges. And the access gives you permission to do anything inside your root directory.
Lunar Pages, on the other hand, charges exorbitantly for shell access.
Inmotion Hosting, however, clearly says that shell access is not available on shared hosting accounts due to security reasons.
If security on a shared host is your priority, choose Inmotion Hosting or something that reputed which doesn’t allow shell access on shared hosting accounts.