I thought i'd share some of the basic links you need for sorting out your Amiga situation.
Forums and help
EAB - English Amiga Board - http://eab.abime.net
To me, this is the best Amiga forum there is. A good mix of both new and old school Amiga users and some very knowledgeable people on board, assure that your question will be answered perfectly (if it hasn't been answered before, use the search option!).
Amiga.org - http://www.amiga.org
This is for the more newschool users, most people here use their Amigas today for everyday tasks. They have them super expanded, so this is the best place to get help with more modern hardware and solutions (like plugging your USB optical mouse to your Amiga, file transfer, video cards, etc.)
Classic WB for Amiga - http://classicwb.abime.net/
These cool guys have sat down to create a full system configuration ready-to-use for your Amiga computer. All you need is some Workbench disks to install this and you will be left with a feature-packed system where you will probably won't need anything else. Great for n00bz of the Amiga, so you won't have t worry if you have this or that library, MUI, AHI or whatever.
Databases
HOL - Hall Of Light - http://hol.abime.net
Do you want information about some game? this is the end-all be-all database of Amiga software. Full of screenshots and tons of other information.
AMR - Amiga Magazine Rack - http://amr.abime.net
If you ever had an Amiga it's more than probable that you were into Amiga mags, and this is the place to get them. Scans of full issues are to be found here and, even though it's mostly dominated by UK mags, otehr magazines are starting to appear. Very cool place to find some tutorials. Magazines com with images of their respective coverdisks too, so you can also find some fab exclusive software.
The Big Book of Amiga Hardware - http://www.amiga-hardware.com/
Found some Amiga junk in a car boot sale and not sure what it is, what is it for, or maybe you need drivers or manuals? This database of Amiga hardware covers almost everything in existence for your friendly computer.
File Repositories
Aminet - http://aminet.net (and many other mirrors)
Aminet is the ultimate Amiga file repository. It's been gong on for ages, before the Internets, so it has a huge collection of stuff. If you need something to get your Amiga up and running, as long as it is shareware or freeware (which most of the coolest tools are) it will be here. An absolute must visit for every Amiga user.
WHDownload - http://www.whdownload.com
If gaming is your thing and you have a hard drive equipped Amiga, this is the site to go. Who isn't tired of floppies? These guys fix games to be ran from floppies, and also patches them to run on newer machines to avoid compatibility issues. There's also a TON of emos in WHDLoad format, so you can see all those trackmos again without worrying if your Amiga is too new or if the floppies haven't gone bit-rot
Music
eXotica - http://www.exotica.org.uk
Anything related to Amiga music will be found here. eXotica is an enormous database of music created with the Amiga (and also featuring otehr formats too, like AY or SID). It doesn't just list the stuff, it's available for download, so if you are looking for some music, it will SURELY be found here. They also host the players for the various types of files available. I recommend you Eagleplayer with every replayer you can get a hold of (look at Aminet )
Stone Oakvalley's Amiga Music Collection - http://www.paula8364.com/
Almost everything you can think of that has been released in MOD format can be found in this website, in both original an MP3 format, the later recorded straight from a real machine for accuracy! They also offer a "MIX" file which makes some better stereo separation on the Amiga's pretty annoying hard panning. This is a must visit for all Amiga music enthusiast.
Shops
Amigakit - http://amigakit.com/
Sometimes you will need to buy something for your Amiga. Even a stupid cable can be almost impossible to get nowadays, so Amiga shops will help you. Amigakit is a bit of a rip-off but some times you have no chance. Have it in mind, they are recommended anyway, I cannot complain about their service, only their prices.
Vesalia - http://vesalia.de
For people in Europe this is probably a better choice. Again, you might be paying through the nose for some items, but not for all, and being an Euro shop, if you live in Europe you will cut down on shipping costs. This shop has been around for a lot of years so they have very good experience in the matter.
Amibay - http://amibay.com/
A forum where people buy and sell Amiga stuff. It's very cool for private transactions ridden of eBay's bloat.
Emulators
WinUAE - http://www.winuae.net
To me maybe the best and most dedicated emulator for any platform, WinUAE (sadly only available for Windows) is an amazing Amiga emulator that retains top notch compatibility for a varied number of models from your standard A500 to newer stuff like an A4000, adding also extra functionality like host system network sharing, "Picasso" graphic card emulation, support for real Amiga hard drives and more. It is an essential tool if you have an Amiga, and it's an awesome alternative if you don't own one. Sound is a bit on the weird side, but now it even has support for ASIO-like drivers for low latency usage, thanks to our request, because Toni Wilen, the programmer of WinUAE, has very open ears to its userbase..
E-UAE - http://sourceforge.net/projects/uaedev/
If you are stuck with no Windows machine to do your living, you will have to use E-UAE. Not even close to WinUAE in terms of compatibility and speed, its goal still is "bringing the features of WinUAE to non-Windows platforms such as Linux, Mac OS X, AmigaOS and BeOS.".I tried it and it;'s not that bad, the major problem is speed but Intel machines should be able to run a lot faster thanks to the JIT emulation technique.
This list will be updated with more data as I remember it.