Redirections and internal redirections are two different things.
An HTTP Redirection with a code 302 or 301 imply several HTTP request and the user will see at the end that he has been redirected to /example.php. An internal redirection means serving one file B on the server for a file A requested, without the user knowing it.
Internal Redirection does not need mod-rewrite's rules. The Alias and AliasMatch directives could be used to map some requested files to a real file.
Alias /beispiel.php /path/to/my/docroot/example.php
External Redirection could also be performed without mod_rewrite, by using Redirect and RedirectMatch directives.
Now you could also use mod_rewrite to perform these two types of redirections (internal & external).
# internal alias
RewriteRule ^beispiel.php$ /path/to/my/docroot/example.php [L]
# Or external redirection, with a R tag
RewriteRule ^beispiel.php$ example.php [L, NC, R=302]
With external redirections qlways Start by trying some rewriteRiles handling 302 redirections. When it will be working you could use 301 redirects as the browser store 301 results and do not ask anymore before restart.
If you have a big number of rediirection to perform and you are not stuck with .htaccess files (i.e. you can edit the real apache configuration files), you could have a look at RewriteMap to speed-up your rewriteRules.