How many types of DNA methylation are there? My current understanding is:


bases A or C can become methylated due to interaction with a methyltransferase
these methylations only occur if the A or C is surrounded by a specific sequence of base pairs
different types of DNA methylations occur in different species at different rates


Is there a comprehensive list of which sequences of base pairs allow methylations to occur? 

I'm currently aware of:


dcm-methylation: CCAGG or CCTGG
dam-methylation: GATC
EcoKI methylation: AACNNNNNNGTGC or GCACNNNNNNGTT
CpG methylation: CG (or CHG or CHH)
If I'm understanding you correctly, by "types of DNA methylation" you mean "nucleotide contexts where DNA methylation occurs".
This is going to be a function of the methyltransferase proteins involved in the methylation process, and this largely depends on the organism, and even cell type being studied.

Generally, what has been observed is:


The phenomenon of DNA methylation (methyl group addition to A/C nucleotides) has been observed in both eukaryotes and prokaryotes
The nucleotide context of DNA methylation differs between the organism, and even the cell type being studied, due to the methyltransferase proteins involved in the methylation process
Methylation of RNA, predominantly in N6 position As


In humans:


The DNMT1 methyltransferase is referred to as the "maintenance" methyltransferase, due to its observation of binding to hemi-methylated CpG sites (methylated C on one strand and not the other)
The DNMT3A/B methyltransferases are referred to as the "de novo" methyltransferases for their affinity of binding to naked DNA
These proteins almost exclusively methylate CpG dinucleotides in human cells
There are cases of non-negligible methylation of cytosines in CHG and CHH nucleotide contexts (brain tissues, for example)


The proteins and their effects on DNA methylation are similar for mice, as well.
Plants tend to have similar nucleotide contexts of methylation, but have much more CHG and CHH methylation than mammals.

In prokaryotes, again, the nucleotide context is dependent on the proteins.
Like you mentioned, we have that:


The Dam methyltransferase methylates the N6 position of the A in GATC
The Dcm methyltransferase methylates the C5 position of the second C in CCAGG and CCTGG
The EcoKI methyltransferase methylates As in AACNNNNNNGTGC and GCACNNNNNNGTT


NEB has a good list of its restriciton enzymes, and how DNA methylation affects their binding/cutting, which also gives some info on the type of methylation in cells.

As for a "comprehensive list", you'll likely have to find some relevant review papers in your organism(s) of interest and compile on yourself.

But also think about how you're phrasing your question.


  Is there a comprehensive list of which sequences of base pairs allow methylations to occur?


I don't think that many papers studying DNA methylation think of the nucleotide context allowing methylation to occur so much as observing the context in which methylation occurs and how it relates to proteins in those organisms.