Most routers are shipped from their vendor with default passwords. And when you login to router administrative interface first time you will need to put this default password in a login form. Usually this password is specified in a documentation which comes together with router.
But the problem is when you don't have documentation available (if you got router as a gift from someone, purchased used router or just lost the documentation). What helps is the fact that default router passwords are the same for each router of certain brand and model. So just by looking up brand and model of the router you will be able to recover default router password and login.
If you think that your router password was changed to a different one and you don't know new password there is one more option left for you: router hard reset. You need to lookup documentation for that specific router and figure out how to do a hard reset (usually you just hold a certain button on a router for a period of time).
Below we're giving you a quick list of most popular router usernames and password which probably cover 90% of all routers. If you router is not there please search for specific model of that router and add word "password" to it. This will probably give you a right answer. We're also working on router password database within this website.

D-Link routers

All D-Link routers use username: admin

D-Link DI-514 and DI-524, DI-804, DI-604, DI-704, use empty password.
All other D-Link routers: admin

Netgear routers

Default user: admin
Default passwords: (empty)
Netgear MR314, RT314 and certain other old models: 1234

Linksys routers

Possible user and password combinations:
Username: admin
Password: admin

Username: Administrator
Password: admin

Username: admin
Password (empty)

Belkin routers

Default username: admin
Default password: none

Netgear WGR614 v4: setup
All other Netgear routers: password