What is the greatest thing Allah (SWT) has forbidden?

The greatest thing Allah (SWT) has forbidden is Shirk (polytheism).

What is polytheism?

Polytheism means to believe that there is one who shares Allah (SWT) in His acts [i.e. ascribing partners or setting up rivals to Allah (SWT) in His rights].

What are the types of polytheism?

There are three types of polytheism:

1. The greater polytheism (Shirk Akbar).

2. The lesser polytheism (Shirk Asghar).

3. The inconspicuous polytheism (Shirk Khafi).

What are the types of greater polytheism (Shirk Akbar)?

There are four types of greater polytheism (Shirk Akbar):

1. The polytheism in invocation [i.e. involving supplications to other than Allah (SWT)].

2. The polytheism in intentions [i.e. purpose and intentions not for the sake of Allah (SWT) but directed towards other deities].

3. The polytheism in obedience [i.e. rendering obedience to any authority against the Order of Allah (SWT)].

4. The polytheism in love [i.e. showing love to others which is due to Allah (SWT) Alone].

What is lesser polytheism (Shirk Asghar)?

The lesser polytheism (Shirk Asghar) is Ar-Riya, that means the acts of worship done to gain praise or fame rather than to please Allah (SWT), this type of polytheism, however, does not cast the person committing it out of the fold of Islam.

What is inconspicuous polytheism (Shirk Khafi)?

The inconspicuous polytheism (Shirk Khafi) implies being dissatisfied with the conditions ordained by Allah (SWT).

What is the proof of the inconspicuous polytheism (Shirk Khafi)?

The proof of the inconspicuous polytheism (Shirk Khafi) is the saying of Prophet Muhammad (SAW):  

"The inconspicuous polytheism (Shirk Khafi) is more hidden among this nation than the track of a black ant over a black stone on a dark night." (Musnad Ahmad)

Are good deeds accepted by Allah (SWT) with the polytheism?

Never!!!  None of the deeds are accepted when mixed with polytheism.  Allah (SWT) says:  

"If they had joined in worship others with Allah all that they used to do would have been of no benefit to them." (Al-An'am 6:88)

"Verily! Allah forgives not setting up partners in worship with Him, but He forgives whom He pleases sins other than that." (An-Nisa 4:116)