Some time ago I've found ATmega88P bootloader but it works fine with IDE 1.0. I would like to use new IDE 1.6 for programming uC (ATmega & ATtiny). I've found ATtiny bootloaders but I can't find the same for ATmega family. Any sugestions for that?
Did you have a custom board in the file "boards.txt" ? I think you have to add that again. The bootloader itself would be the same for 1.0 or 1.6.0 However, taking just any bootloader from the internet might not be a good idea. You have to check the fuses and settings and which options are used to create the Optiboot bootloader.
Optiboot supports atmega88, but there is no pre-built .hex file; you'll have to make it yourself. In 1.0.x, you could do this by connecting to .../hardware/arduino/bootloaders/optiboot and typing "./omake atmega88" (or ".\omake atmega88"), but it looks like 1.6.x no longer includes the "make" utility :-( (or any make utility.)
If you have an avr development environment installed in your path, you should be able to do "make atmega88"
As Peter says, the bootloader(s) have not changed since 1.0 (actually, I take that back. The source code sent out with 1.6 is still optiboot 4.4, and I don't think it will compile correctly using the new compiler (4.8.x) that also comes with 1.6.x; you'll need to either have an older compiler, or new optiboot source (from https://code.google.com/p/optiboot/))
I compiled an Optiboot 5.0a with Arduino IDE 1.5.8 with the new compiler. But I had to change the path to the tools. I don't know anymore how I did it, but it compiled and it worked. The ATmega88 has 'P' and 'A' options, those might have a different signature.