Booking & Reservation System
This would be really tricky without a plugin but you could (and this is a stretch) manipulate the entry channel to accept "reservations" where as the reservations date and time use the date and time field types.

You could then output all the reservation entries to show if/when times are still available. There's no getting around this though, you'd need to work extensively with the saveEntry form, jQuery and a date/time picker to get everything to line up correctly.

The best way to do would be to create a reservation plugin that does specifically this instead of wrangling entires to do the same thing. Either-way I'd say you're looking at some in-depth development time.