This article is from the Amiga FAQ, by Ignaz Kellerer with numerous contributions by others.
Motorola, the company producing the 680x0 family offers crippled versions of their processors. They are a little bit cheaper than the originals, that's why Commodore decided to build the 68EC020 into the A1200 and the 68EC030 into the A4000/030.
The difference between the 68020 and the 68EC020 is that the latter can address just 16Mb of memory. That's why the A1200 cannot have more that 10 Mb RAM. In most cases you will not notice the difference.
This is not the case for the 68EC030: Many owners will notice that the 68030 has an MMU and the 68EC030 doesn't have. There are some important programs depending on an MMU, for example Enforcer (a debugging utility), GigaMem (a program to emulate virtual memory) or all current Unix versions (see Unix). Other Amigas than the A4000 and the A3000 need an additional processor card using a 68030 or 68040 or 68060 to run these.
Finally the 68LC040 is a 68040 without FPU. See FPU.