I don’t have a lot of time, today, but I’ll put my money where my mouth is, as the saying goes - here’s some more for you…
Call Retrieval - goes with call parking, your definition is a little murky; Call Park allows you to place a call on hold on an extension other than your own. This is useful for retail stores or factory floors, where you may need to page for the correct person to pick up the call, which is called Call Retrieval.
Call Waiting - allows the use of a hook-flash to change between two simultaneous calls
Dial By Name - assuming voicemail is set up correctly, Dial By Name allows an outside caller to get 411-like help in finding the extension number of the person they wish to call
Direct Inward System Access (DISA) - allows an outside caller to have full access to PBX functions, which is normally reserved for internal-only access. Common use of DISA is if you have road warriors or home-based workers: they can call into your PBX and make free outbound long distance calls, also appearing to be at your physical location
Distinctive Ring - Asterisk can allow you to change the ring frequency (and sometimes tones) usually based on CallerID of the incoming call, but can be set based on other variables. Useful for call-screening, among other things
Macros - In configuring the dial plan, the use of macros and pattern matching greatly simplifies identical configuration for hundreds, even thousands, of extensions.
Predictive Dialer - generally for use in outbound telesales or customer service; predictive dialing optimizes the time that agents spend on the phone by pre-dialing numbers when it is determined that an agent will be coming available.
Overhead paging - sometimes also called intercom, this allows a centrally-located speaker to be “dialed into,” for making announcements. Frequently seen in retail stores, also car dealers, factory floors and other non-office type situations
Protocol Conversion - can bridge calls between dissimilar systems, for example IAX to SIP, PSTN to MGCP
Spell / Say - can “read” letters and numbers to a caller, for example reading back the current time
Streaming media access - especially because of Asterisk’s open nature, you can stream certain types of media, for example mp3 music, directly into the phone system. Useful for “live” hold messages, et al.
Supervised Transfer - similar to blind transfer, allows a person to transfer a call to another extension by first announcing that call to the transfered extension. Useful in situations like “I have Joe Carseller on the phone, do you want to talk to him?”
Talk Detection - there are a few modules which allow various types of noise detection on certain channels; talk detection can be used to trigger an event, for example, play an automated message when somebody says “hello.”
Text-To-Speech - using the Festival voice synthesis suite, the PBX can read text, for example a web page containing the current weather or an email
Time and Date - unclear; some of the voice protocols (including, I believe, T1/E1 services) allow time sync between various terminations. Voicemail is automatically timestamped, and the system will read back the envelope, which includes time and date (optional). Also, see Text-To-Speech and Say/Spell, above.
Transcoding - This refers to the ability of Asterisk to bridge calls that use different audio encodings, for example g711.u to GSM
Trunking - logically grouping together multiple phone lines for outbound dialing; typically seen in medium to large deployments, the PBX can be configured to auto-select an available line for outbound dialing, rather than the user having to choose which line to dial out on.
VoIP Gateways - Asterisk can act as a bridge between VoIP telephones and the PSTN; additionally, Asterisk can be used to route calls to some third-party VoIP gateways (think Vonage, though I don’t believe that is an available option). Check out BroadVoice or Packet8.
Voicemail to email - Asterisk’s native voicemail can send an email to the voicemail recipient, and can optionally attach a WAV file of the entire message.
Web Voicemail Interface - as with most things Asterisk, it is almost trivial to provide a browser-based interface to the system
Zapateller - built-in, automated “black hole” for inbound telemarketing calls