Paranoia is a wonderful thing !
Somdcomputerguy is quite right insofar as he goes - that will tell you if someone is connected at the time you are looking, but that isn't really your problem, is it ? What you want to know is if anyone can connect through your router.
Borrow a laptop, or get a friend to come round with theirs, and see if it can connect through your router without inserting passwords or security keys. If this laptop can connect, you have a problem - an unsecured network. If they can't, you may be good to go.
You say your router has a password set. The problem is that there at least three different passwords possible on a router, and it is not clear which one you mean. The first is the one to access the router control panel, and this usually comes, by default, as either 'admin' or 'password' depending on the maker. This is easily changed on accessing the router control panel, and mine is set to somethng like 'crocoDile'. The next one is the password issued by your ISP which, along with your telephone number, is used to access their services from the router. This is normally a very strong password, ie a random string of letters and numbers, and you can't usually change it. Just keep a note of it it in a safe place.
The third one is the router security system.
At a mininum, you should have WEP enabled, and for a strong preference, WPA-PSK. This you can set up by accessing the router control panel and selecting the security of your choice. You then need to generate a security phrase which then becomes your access code. KEEP THIS IN A SAFE PLACE, UNLESS IT IS VERY MEMORABLE ! Once you have set this, any computer trying to access your network needs this code phrase to do so. The only downside to this is that every computer on your network has to be set to the same security level and the same security code, but this is a very small price to pay.
Prevention is better than cure !
Chris Cosgrove ( Certified Paranoid )