Editing Wikipedia with an IP address as your identifier is often less anonymous than editing with a normal account.
Why is this the case?
Your IP address usually links you to an Internet Service Provider (ISP), and that often links you to a particular geographical location, or to a particular company. Internet tools such as WHOIS and Reverse DNS lookups may identify you, your employer or school, or computers that use your address, including mail or web servers. All of these provide mechanisms for curious individuals to determine where you live or who you are. This is more information than is available about an editor who registers an account and uses the account name instead of an IP address to sign their edits.
Exceptions
If you edit from an Internet cafe, a library, or another public Internet access point, or if you edit while travelling, your IP address may say very little about you. If you edit through a proxy, your IP address will be that of the proxy server, rather than your own. Note that editing Wikipedia through Virtual Private Networks, anonymizing proxy servers, or Tor is, at a minimum, controversial, and users editing via these proxies are most of the time blocked from editing, until you disconnect from anonymity networks due to problems of vandalism on anonymous networks such as Tor, proxies, and VPNs.
Second-class treatment of IP address editors
Some registered Wikipedia editors and administrators treat IP address editors as (at best) unwelcome party-crashers or as potential vandals. Some ignore the opinions or revert the edits of IP address editors simply because they are "anonymous". There is no Wikipedia policy which supports this treatment, and there are several long-term and constructive Wikipedia editors who edit solely under a fixed IP address.
The treatment of IP address editors as second-class editors is counter to Wikipedia policy and the spirit of anyone-can-edit collaboration.