have it redirect to my Twitter page instead, or maybe some other, free blog hosting
For both these examples you probably don't have the power to make your domain known to whoever is hosting those services. And the target URL is not a domain, but includes a path.
So, the following is not an answer to your question, but just to explain why this cannot be done using plain DNS. Or: why it cannot be done while keeping your domain name in the URL (unless you would use some redirection in a frame, but then the URL does not change when your visitor goes to another page).
As for the domain: currently Twitter does respond to whatever maps to its IP address. Like twitter.com, 168.143.161.20, but also example.com if you map that domain to the same IP address. (You could test that using your hosts file on your own computer.)
However, some sites might not accept unknown host names, or may show some other default site. Like for youtube.com, 74.125.77.139 does not show YouTube because the browser does not specify Host: youtube.com in the request, which makes the web server respond differently even though YouTube does use that IP address:
host www.youtube.com
www.youtube.com is an alias for youtube-ui.l.google.com.
youtube-ui.l.google.com has address 74.125.77.139
youtube-ui.l.google.com has address 74.125.77.100
[..]
As for the path: in a DNS you cannot map a domain to another domain including a path. So, you cannot set up a DNS to map example.com to twitter.com/example.
You would indeed need some refresh redirection like Wil described, or some third-party service that does that (or something called "HTTP 301 moved permanently") for you.