Better aligner than bowtie2? Bowtie2 is probably the most widely used aligner because of it's speed. Burrow-wheeler (BW) algorithms (including bwa) tend to be faster. However, they have limitations when it comes to aligning very short reads (e.g. gRNA). Also, setting maximum number of mismatches allowed is complicated by the seed length, overlaps and other parameters.

I wonder if there is any better multi-purpose aligner out there. May be with algorithm other that BW. One which allows special cases e.g. allowing shord reads and high number of mismatches.
Bowtie2 is no longer the fastest aligner. Salmon and Kallisto are much faster, but have been designed to optimise RNASeq mapping. Their speed is gained from avoiding a strict base-to-base alignment, but they can output mostly-aligned reads (i.e. position-only, without local alignment) as pseudo-alignments. See here for more details.
Both Kallisto and Salmon can do additional bootstrapping that is interpreted by sleuth for improved performance in isoform detection. They can also output counts that are equivalent to read-level counts from other programs, which can then be used by other downstream gene-based differential expression analysis software (e.g. DESeq2). Salmon has additional options that can  correct mappings for sequence-level and GC bias.
HISAT2 is from the same group as Bowtie2, and does the same sort of stuff, but with a few optimisations added on top. In particular, it's much better at working out split reads from RNASeq runs. Like Bowtie2, it will do local alignment of reads.
For quick alignment of long reads, minimap2 works well. For high-accuracy alignment (but comparatively slower), LAST works well.
Most bioinformaticians seem to prefer STAR for things that Bowtie2 was previously used for. I'm not yet convinced it's a better alternative, and currently prefer HISAT2 for high accuracy short-read alignment.