If you run one application at a time, then there is 0 advantage. If you like playing music, browing the internet, viewing emails, having 6 IM programs on, having a torrent client on, having 25 update routines, an antivirus program AND a game/video on at the same time? Then having extra RAM will increase the number of simultaneous programs you can run before your computer/laptop slows down to a crawl.
Also, Windows itself tends to use between 500MB-2GB of RAM, depending on how much is available (it tries to scale). Needless to say, you'll need 64bit Windows to take advantage of more than 3GB of RAM.
EDIT: As for laptop brands, most have plenty of high end powerful laptops, mid ranged business laptops and low end ultra-portable netbooks (and budget laptops but they tend to suck). If you go for Sony VAIO or HP Pavillion, you'll find that you tend to have to pay slightly more than Samsung or Acer. You can customize/build your own laptop using internet tools provided by sites like Dell/Alienware, MSI or XoticPC (I think that was the name - I don't usually use American sites) to try and create something exactly to your needs, but you may end up paying more for the service than you normally find for prebuild/noncustomizable laptops.
Think of what you want, think of what you need (i.e. cross out the things you don't), then think of what you're willing to pay (and how much to compromise). Finally, look at the actual company websites to get a good idea of what type of laptops they offer and how they cater to your needs.
