Why Alfred over Spotlight Search? They appear to be the same thing.
I know others have answered this already, but just a sampling of how I use Alfred pretty much every day at work (usually hundreds of times per day).
<smoosh>-V ("smoosh" meaning the three modifiers on the left side all held down - control-option-command) = pick from recent clipboard items to paste in
shift-<smoosh>-V = paste whatever is on the clipboard in plain text (no formatting)
shift-<smoosh>-L = Display whatever is highlighted on the screen in large text so I can see it from across the room. You can get the same with <smoosh>-space "whatever", Command-L, but this little mini-workflow us more commonly used for me.
<smoosh>-L = open a new Terminal window and 'less' through the highlighted Finder/PathFinder file
<smoosh>-space, "bug" look up the bug number(s) I copied to the clipboard in our bug tracking system (opens a Safari window on our Jira instance with either the bug or search results of all copied bug numbers; note that I can skip the keyboard on this and the others by typing in after "bug" like "bug esc-1234", but usually I am looking up a bug that someone sent as text so it goes to the clipboard instead of being typed in)
<smoosh>-space, "cl" look up the changelist(s) I copied to the clipboard in our code review system
<smoosh>-space, "cve" look up the CVEs I copied to the clipboard in the National Vulnerabilities Database
<smoosh>-space, "smb" take the SMB address (possibly in Windows format, which auto-converts to smb://... format) and open it using Finder
<smoosh>-space, "movie Star Wars" - open searches (in three tabs) of YouTube, IMDB, and RottenTomatoes on the given movie title, which is a godsend when scrolling through ex the Apple TV Netflix app which doesn't give any kind of "how good is this movie really" indication other than its wonky "90% match" judgement.
Then there are search keywords like "hulu", "prime", "usps", etc, which search in specific systems, the simple calculator ("What is 17*37?" => <smoosh>-space, "17*37", answer displays below and I can hit 'Enter' to copy to clipboard of Command-L and flip the screen around to display the answer in large print), the dictionary and spellcheck (<smoosh>-space, "define bugaboo" shows the definitions as well as the ability to open Dictionary on it; <smoosh>-space, "spell cieling" shows the corrected spelling as well as the definition of the suggested word), the snippet management system, etc.
Alfred is a workflow/automation app, not just a search app. It is also great at local search (and tends to find stuff better than Spotlight especially for new apps on the system.
For "essential for me apps", Alfred (and the setup I have for it) is the thing that is most critical after the OS itself. Spotlight Search doesn't even come close to replacing Alfred.
Could QuickSilver do all this? Back when I used it, it wasn't there yet, but maybe it could nowadays. As someone else mentioned, QuickSilver had its moment in the sun, then when it was abandoned for some time I looked for alternatives and Alfred was there. I see no reason to look back to QuickSilver at this point unless there are some major killer features it has which Alfred does not.