Many ISPs, Universities, or other organizations have policies that limit the usage of peer to peer applications for their customers, students and employees. Typically, these policies block or limit the amount of bandwidth that P2P applications can use, and are enforced by packet analizing solutions from Blue Coat or a similar company. This software/hardware solution has the ability to look into a TCP packet, determine what class of application created it, then throttle or block it accordingly.
If you use DC++ from an organization and you're behind such a block, please learn to live with it. Circumventing the block by proxying is detectable, is probably against your AUP, is technically difficult, and impossible to do without help from someone outside the firewall.
If your ISP blocks or (heavily) throttles P2P connections then you'd better to change to another available provider which does not use (unacceptable heavily) P2P throttling or blocking techniques.
You can also try to log on to hubs using the ADC protocol. Since this protocol is fairly new you have a high chance that the blocking hardware or software can't recongnize it. You can find ADC hubs in the configured hublists come with DC++ by default. The address of an ADC hub always starts with adc:// or adcs:// so puting these to the Filter box in the hublist window will show you the available ADC hubs right away.
Other organizations might have their network behind a NAT in which case an active connection is impossible. There are also ISP's offering such kind of access mode (firewalled access). If you're inside a NAT, the IP reported by your computer will be in one of the non-routable IP ranges. In this case, try passive mode.
If you cannot connect to DC hubs or cannot transfer files in passive mode, the above advice about proxying applies.
A few organizations use simple port blocking, where common ports used by DC++ and other p2p applications are blocked. DC++ uses a wide range of ports for outgoing traffic and incoming traffic by default. If the school blocks port 411 outgoing connections, then that effectively cuts you off from all DC hubs since that is the default hub port. Hub lists contain the full address of many hubs and those that run on non-standard ports (i.e. hub.example.com:1411) may work. Some ISPs (according to the IANA recommendations) may not allow all ports for incoming P2P transfers. In this case you need to choose any port within the region of 49152 - 65535 for the port fields in the Connection Settings.
If you appear to be completely blocked from the DC network, the above advice applies.