Warning: Noob question.

I am not sure, but I think there must some way to see Internet behaviors of other computers on the same router.
Is there any way to "hide" yourself from others on the same router?
Is a firewall enough?
Or, am I just being paranoid?

I did try to search this on Google, but most results were about security problems from outside.

Thanks

There is -- it's called packet sniffing.  However, it is sufficiently complicated to make it extremely unlikely your roommates, neighbors, family members, or whomever you are afraid of, would be doing that. 

If somebody told you they are monitoring you, they are probably just pulling your leg.  If not, it is much more likely they've had physical access and installed some monitoring software on your computer.  That could range from simple key loggers to crap like this.  Reformatting and a clean Windows install will get rid of all that.  Of course, if you are living with the culprits, it may be difficult to keep them from doing it again.

Assuming there is sniffing going on, the only effective protection against it is encryption.  Some protocols are encrypted by design (for example HTTPS, which you use when you access "secure" sites, such as online store checkouts).  If you are concerned about Messenger conversations, there is an add-on available, but it also has to be used by the people you talk to for encryption to take place.

You could potentially encrypt all your Internet traffic by using a VPN tunnel to a network at another location that you trust, but that is probably not a practical option.

It's quite possible to get past a firewall or even a secure connection (HTTPS or other SSL) if the attacker uses an exploit known as ARP Poison Routing. Every computer on your network is represented by a MAC address, not an IP Address. IP Addresses are mapped out to MAC Addresses in a table in both your router and every computer on the lan. You can see this table by running "arp -a" in windows' command prompt. Anyway, if someone else on your LAN were to send signals to you and your router saying "I'm XXXXX IP," then all of the data would suddently be going to them. A little re-routing, and all of a sudden you've got an easy way to monitor someone's traffic over a LAN.

What kind of router is it? If it's not a normal PC (it's a little proprietory box), then it will be difficult for other clients to see what you send through the router. If it is a PC (or other flexible platform), then logging traffic will be easier.