Your InDesign, Fireworks, Photoshop and Dreamweaver files should open up fine.
The question would be what fonts you're using. Hopefully, you're using OpenType or TrueType fonts. If you have a lot of files with old PostScript Type 1 fonts, you'll need to re-buy or replace fonts because T1 fonts have different formats for Mac and Windows.
Thanks Steve thats good to know, hadn't thought about the fonts but that wont be a problem
Files are cross platform compatible.
However, you may have issues with line endings being different.
The Type Engine in indesign is updated each edition, and from CS3, CS4, CS5, CS5.5 and CS6 that's a quite a lot of updates to the Type Engine.
You may experience some type issues here where the line endings don't exactly match to the last versoin.
And you won't know until the text recomposes, which it doesn't do automatically, but only after you select text or a text frame, so be careful.
Also I STRONGLY recommend you export all of your CS3 files to .inx while you still can and open the .inx versions in CS6 rather than opeing the CS3 .indd files. We see too many reports here of problems that develop with directly converted legacy files in CS6. It doesn't happen to all files, but you can't predict which ones will develelop a problem, and the problems often don't show until you've done considerable work.
Peter Kahrel has a good script at http://www.kahrel.plus.com/indesign/batch_convert.html that can batch convert to a variety of formats, including CS3, and Kasyan Servetsky has another one at http://kasyan.ho.com.ua/batch_export_to_interchange.html