just to expand on DopPie's answers for anyone new to the Amiga:
I added a scandoubler. Why? It enables me to use VGA monitors.
The Amiga flickers like a bastard in high resolution (hi-res interlace PAL or NTSC, TV modes basically) - and those game modes won't work on a standard VGA monitor without having the refresh rate doubled (by a scan doubler).
If you own an LCD TV that scans at 50/60 this won't be a problem, it should handle it just fine.
Most games are in low resolution anyway , so they won't flicker on a TV, but won't display on a standard PC monitor.
I added an 68030 accelerator. Why? Cause it allowes me to compile / (de-)comress files faster.
You can also play games that are helped by an acelerator, FPS games and PC ports in particular, but some flight sims like TFX and and shadow of the 3rd moon as well.
Amiga Demo scene stuff looks great on accelerated machines.
Work bench will respond faster, and can be made to look nicer, and workbench 3.5 and 3.9 will run.
If your into retro APPS as well as games, there's loads of old packages that will benefit.
You can (just about) play MP3 on an 030 50mhz, and you can easily play all those lovely PC MOD tunes that are out there.
Master system, ZX spectrum, MAC, c64 and gameboy emulation should play ok.
I added 32MB of RAM. Why? Cause it allows me to load lots of stuff at the same time.
As above, don't get an accelerator without ram, but get RAM on its own if you just want to run WHDload to run standard A1200 and A500 games, and don't care about higher end games and demo's.
I added a compact flash adapter. Why? Too be transfer files between PC/Amiga.
You can also add a compact flash as a HDD. The amiga will boot faster, respond better than a 2.5 inch HDD, be silent, and drain less power (important if you are still using the standard A1200 brick).
Iv'e also had a 3.5inch HDD in mine, but you have to bend back a bit of the internal shielding, and buy a new cable. It's faster than a 2.5in HDD, but a real power hog. My compact flash card seems a lot faster.
I added a NIC? Why? For networking ofcourse.
Sweet, you can also add wireless, if that's your poison, through the PCMCIA port on the side.
I'm going to add my newly acquired 68060 accelerator. Why? See 68030 accelerator and multiply that by 4 (or more?).
I'm going to add extra cooling for the 68060. Why? So it may live longer
Some games, and many demo's will benefit greatly from an 060, which runs cooler than an 030, and much cooler than an 040. It should not need a fan, unless you clock it . A 50mhz 060 should be about 5 or 6 times faster than an 030 at 50mhz. Easily able to play MP3's.
Also remember that full Mac os 7.5 to 8 emulation is possible. It's very fast in CPU terms, as its more like WINE than an emulator, you could always try some mac web browsers (although graphic refresh is a bit slow without a graphics card....I wish someone would create a trapdoor graphics chip and accelerator combo!)