The most famous manufacturer of computer processors is IBM. The most famous manufacturer of computer processors after IBM is AMD.
This is a bit of a confusing question. IBM-Compatible computers are a type of microcomputer themselves. Any x86 based processor, such as AMD, Intel, VIA, and Cyrix, are IBM-Compatible. Other systems also exist, such as older Macs which used IBM PowerPC processors and Motorola processors. There also exists Sun Systems SPARC processors, and a whole host of others. IBM-Compatibles are the current dominant consumer system.
IBM does not make laptops. IBM makes processors that are used in computers, but not actual computers. So the answer to your question would have to be Dell.
Apple worked with IBM and Motorola to develop the Power PC processors which were a development of IBM's POWER1 processor. Apple used Power PC processors in their range of Macintosh computers between 1994 and 2006 when Apple switched to using the processors from Intel's range. IBM produces a range of processors for all types of devices including the Cell processor used in Sony's PlayStation (The X Box also uses a Power PC processor). (See links below) In 2008 Apple spent $278 million to acquire PA Semi a company which designs processors based on the Power PC model. It is not known what Apple intends to do with processors designed by the company.
IBM And Microsoft
IBM AIX currently only supports Power chip processors, which are not the Intel X86 format.
MS-DOS
IBM AIX was created in 1986.
IBM CPC was created in 1949.
IBM Award was created in 1984.
IBM JX was created in 1984.
IBM SSEC was created in 1948.