I have a router(with wire). Shared by a computer and a laptop. Now, I'm pissed of every time the other party(laptop) uses the connection because my downloads slows down. Is there any way I could have more bandwidth than the other party.
Give your computer higher priority in the router's QoS settings. This will give your packets priority at the router level. Setting this is up is dependent on your router's firmware as each is slightly different.
If you have access to the other machine, which I'll assume is using Windows, you can install Traffic Shaper XP (freeware) or NetLimiter on it and limit bandwidth that way. Keep in mind only the paid versions of NetLimiter offer shaping. Trickle should work for most other systems.
Of course, each solution can be circumvented depending on how tech savvy the user of laptop is.
If you own the network you could use ARP spoofing to trick your network into thinking that your PC is the internet gateway (i.e.router / modem), then all traffic headed for the internet will go to your PC.
Technically, this only affects outbound traffic, but as it happens this is usually 90% of the problem.
So if you setup your PC to do traffic shaping as John T suggests, but don't have access to the other PCs you could use ARP spoofing to deceive the other machines on your network into using your traffic-shaping-PC whether they want to or not.
I used to use this trick when I wanted to use Skype when my housemates were away for the weekend and left there machines torrenting.