Is the quality score of fastq used somewhere besides trimming/fastqc? In the fastq format every 4k+4-th line contains the positionwise qualityscore (ascii encoded):

@SEQ_ID
GATTTGGGGTTCAAAGCAGTATCGATCAAATAGTAAATCCATTTGTTCAACTCACAGTTT
+
!''*((((***+))%%%++)(%%%%).1***-+*''))**55CCF&gt;&gt;&gt;&gt;&gt;&gt;CCCCCCC65 
...


which program uses this information besides trimming tools (cutadapt) or quality control (fastqc)?

I heard that segemehl (mapping) abandons this quality string in favor of running time (maybe other mapping tools too?)
But what about abyss, trinity, ...? 

UPDATE:

So i atrifically generated a fastq file containing 2 identical reads that perfectly match a sequence in some genome (C.fna). 
The two reads have the most extreme phred scores (only '!!'=highest sanger phread and only 'II'=lowest sanger phred)

Now using segemehl the mapping quality is identical (60)

@HD VN:1.0
@SQ SN:C_fna    LN:15440
@RG ID:A1   SM:sample1  LB:library1 PU:unit1    PL:illumina
@PG ID:segemehl VN:0.3.4    CL:segemehl -i C2.fna.idx -d C2.fna -q test.fq
A   0   C_fna   261 60  220=    *   0   0   ACAGGAAACACAGAAAAAAGCCCGCACCTGACAGTGCGGGCTTTTTTTTTCGACCAAAGGTAACGAGGTAACAACCATGCGAGTGTTGAAGTTCGGCGGTACATCAGTGGCAAATGCAGAACGTTTTCTGCGTGTTGCCGATATTCTGGAAAGCAATGCCAGGCAGGGGCAGGTGGCCACCGTCCTCTCTGCCCCCGCCAAAATCACCAACCACCTGGTG    !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!    HI:i:0  NH:i:1  NM:i:0  MD:Z:220    RG:Z:A1 YZ:Z:0
B   0   C_fna   261 60  220=    *   0   0   ACAGGAAACACAGAAAAAAGCCCGCACCTGACAGTGCGGGCTTTTTTTTTCGACCAAAGGTAACGAGGTAACAACCATGCGAGTGTTGAAGTTCGGCGGTACATCAGTGGCAAATGCAGAACGTTTTCTGCGTGTTGCCGATATTCTGGAAAGCAATGCCAGGCAGGGGCAGGTGGCCACCGTCCTCTCTGCCCCCGCCAAAATCACCAACCACCTGGTG    IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII    HI:i:0  NH:i:1  NM:i:0  MD:Z:220    RG:Z:A1 YZ:Z:0
[SEGEMEHL] Thu Feb  6 08:35:15 2020: matching w/ suffixarray has taken 0.000000 seconds.


So segemehl does NOT use the read quality phred (basically only using the read sequence for mapping)
I think almost all alignment programs would use base quality as a factor to calculate mapping quality (See here). These would also be used in Variant Calling to pick reads where high quality bases confidently align as either the reference base or one of the alternate bases.