I found this article online which shows how to create a visualforce email template, that can send an email with an ics attachment.

http://developer.force.com/cookbook/recipe/creating-email-templates-and-automatically-sending-emails

<messaging:emailTemplate subject="Received your resume" 
    recipientType="Contact" relatedToType="Job_Application__c">

<messaging:plainTextEmailBody >
Dear {!relatedTo.Candidate__r.First_Name__c}  
        {!relatedTo.Candidate__r.Last_Name__c}

Thank you for your interest in the position 
        {!relatedto.Position__r.name}

We would like to invite you for an interview. 
Please respond to the attached invitation.

Regards,
Company
</messaging:plainTextEmailBody>


<messaging:attachment filename="meeting.ics" 
        renderAs="text/calendar; charset=UTF-8; method=REQUEST">
BEGIN:VCALENDAR
METHOD:REQUEST
BEGIN:VTIMEZONE
TZID:(GMT-08.00) Pacific Time (US and Canada)
BEGIN:STANDARD
DTSTART:16010101T020000
TZOFFSETFROM:-0700
TZOFFSETTO:-0800
RRULE:FREQ=YEARLY;WKST=MO;INTERVAL=1;BYMONTH=11;BYDAY=1SU
END:STANDARD
BEGIN:DAYLIGHT
DTSTART:16010101T020000
TZOFFSETFROM:-0800
TZOFFSETTO:-0700
RRULE:FREQ=YEARLY;WKST=MO;INTERVAL=1;BYMONTH=3;BYDAY=2SU
END:DAYLIGHT
END:VTIMEZONE
BEGIN:VEVENT
DTSTAMP:20090921T202219Z
DTSTART;TZID="(GMT-08.00) Pacific Time 
        (US and Canada)":20090923T140000
SUMMARY:Invitation: Interview Schedule @ Wed Sep 23 2pm - 4pm 
ATTENDEE;ROLE=REQ-PARTICIPANT;PARTSTAT=NEEDS-ACTION;RSVP=TRUE;
        CN="{!recipient.name}":MAILTO:{!recipient.email}
ORGANIZER;CN="John.Smith":MAILTO:recruiter@company.com
LOCATION:Hawaii 
DTEND;TZID="(GMT-08.00) Pacific Time 
        (US and Canada)":20090923T160000
DESCRIPTION: You are invited to an inverview
        \NInterview Schedule
        \NWed Sep 23 2pm - 4pm 
        (Timezone: Pacific Time) \NCalendar: John Smith 
        \N\NOwner/Creator: recruiter@company.com   
        \NYou will be meeting with these people:
        CEO Bill Jones, 
        Office Manager Jane Jones
\N
SEQUENCE:0
PRIORITY:5
STATUS:CONFIRMED
END:VEVENT
END:VCALENDAR

</messaging:attachment>

</messaging:emailTemplate>

The problem I'm running into is assigning the DTSTART and DTEND values from a Date/Time field on a record. When I put the field there, I don't think it's in the correct format, and even if it was, I think it's showing as GMT.

Does anyone have advice or have worked with something like this in the past?

Thanks!