At nearly 5 million listings, the ODP is the largest directory on the Net (if you discount copies of the ODP which add sponsored listings or other listings of their own.) Only Yahoo! and Looksmart are/were in the same league i.e. having millions of listings. Looksmart is now broken up into sections each on its own domain.
Yahoo! and Looksmart are both heavily commercial, so the ODP is really in a league of its own. Other non-commercial directories are far, far smaller.
Importance can be calculated in different ways though. The ODP is free to use on other sites (under license). Among its clones is the Google Directory, which almost certainly gets far more traffic than its parent. My site certainly gets more referrals from the Google Directory and one or two other ODP clones than from the ODP itself. However use of the ODP itself has risen steadily over the years, according to Alexa. How much of that traffic is from submitters and editors, and how much from searchers, I couldn't say.
The use of directories for search has declined since the rise of Google and other reasonably effective search engines. However the ODP is used by search engines in various ways. For example a link in the ODP is likely to be picked up fairly quickly by the SE robots and the site will be indexed.
I want to stress though that a link on any other site that is regularly visited by all the major SE robots would have exactly the same effect. It is not necessary to be listed in the ODP to become visible in the search engines.