What is the most powerful kind of parser? As a side-project, I'm writing a language using Python. I started by using a flex/bison clone called Ply, but am coming up against the edges in the power of what I can express with that style of grammar, and I'm not interested in hacking up my language because of an impedance mismatch with the tool. Therefore, I'm not averse to writing my own.

So what's the most powerful type of parser? Citations to papers (as well as more introductory articles) would be welcome.

(I know that 'powerful' is not precisely defined, but let's be a little loose with it and see where the answers go)
A grammar is usually defined as a Context Free grammar - a precise definition is given on the Wikipedia page, but it works the same as it does in PLY, which is based on Bison, which is in turn based on yacc.

It says here that PLY uses a LALR parser. This is essentially an LR parser where the lookup tables are condensed, possibly introducing parsing conflicts, reducing some of the expressiveness of an LR grammar (ie, a context free grammar that an LR parser can parse). If you want to know about the limitations of this particular branch of parsers and those of other parsers, an overview of all kinds of parsing techniques (LL, LR and others) is given here.

To answer your question: there exist parsing algorithms capable of parsing any context-free language, even if the language is ambiguous (ie, there is more than one way to interpret the input):

The first such algorithm was the CYK algorithm, which unfortunately has a running time of $O(n^3 |G|)$, where $n$ is the length of the input string and $|G|$ is the size of the grammar and is therefore impractical for parsing languages.

The second algorithm is the Earley algorithm. This algorithm is also capable of parsing any context free grammar. Although the algorithm needs $O(n^3)$ time to parse an ambiguous language, it only needs $O(n^2)$ time to parse an unambiguous language. In addition, it apparently works in linear time for most LR grammars and works particularly well on left-recursive grammars.

Here you can find a paper discussing a practical implementation of (an adaptation of) the Earley algorithm. They conclude: "Given the generality of Earley parsing compared to LALR(1) parsing ((which is roughly what PLY does)), and considering that even PEP’s ((their implementation of Earley's algorithm)) worst time would not be noticeable by a user, this is an excellent result".

The last type of parser is the GLR parser. This is a generalised version of LR parsing, capable of parsing any context-free language.

A mature implementation of GLR is ASF+SDF. Bison can also generate a GLR parser, though its implementations is slightly different from the 'standard' GLR algorithm. The Elkhound Algorithm is a GLR/LALR hybrid algorithm. It uses LALR when possible and GLR when needed, in order to be both fast and capable of parsing any grammar.

Beyond context free grammars there are context sensitive grammars, but these are in general hard to parse and don't add that much expressiveness: you can do more with them, but for most applications the extra uses are not relevant, unless you're parsing a natural language.

As the final step there are unrestricted grammars. At this point the grammar is Turing-complete, so there is no bound one can give on how long it will take to parse a particular language, which is undesirable for most parsing applications. The extra power is almost never needed. If you do want to use all that power, there is the language machine available.

Lastly, implementing your own parser-generator is not a trivial affair, in particular to get it to be fast. I've personally just finished making my own version of flex (the lexer generator), and while this seemed like an exercise in relatively simple algorithmic problems, it became quite complex to get right, in particular when I tried to support Unicode. Consider using an already existing implementation instead of writing your own.