Yes. We recommend buying not only your domain name with your favorite extension (eg. .com), but also additional, alternative domain extensions (eg. .net, .info, etc). The reason is simple. Having more than one domain extension strengthens your online identity, secures your brand name and improves your online presence. Buying more than one domain extension also protects you from your competitors registering your additional extensions and enticing away your customers.
The longer your domain name is, the harder it is for people to remember it and the more chance you have of someone misspelling one of the words. Most good single word domain names are long gone, but you can still avoid long domain names by getting a little creative. If you have a single word you really like that is not available, try adding an adjective or verb in front of it and seeing if those variations are available. Think of your domain name as part of your brand, and make sure it matches how you want people to think of you.
A short, one-word name (ex. cat.com), and especially .com domains, will be pricy because simple titles have a lot of potential uses, meaning people probably already check them out on their own. If you are going after a registered .com domain, you will have to contact the current owner, and even then, prices could be high for misspellings and multiple word domains. In the past years, companies and individuals have settled for bizarre names, misspellings, and old tricks like adding “the” or “my” to the front; note, however, that this will also reduce domain performance.
When looking up a bare name in DNS, the network stack will add the search domains to it to form fully qualified domain names, and look up those as well. For example, if the domain search list contains "wikipedia.org", typing "en" in the browser will direct the user to "en.wikipedia.org". Some ISPs add their own search domains via DHCP settings, similar to how they add DNS servers and other networking information; if this is undesired, the user can change this setting to ".local".