Most of the eSTREAM finalists (http://www.ecrypt.eu.org/stream/index.html) are not block-based. I think only Salsa20 matches that description.

More generally, I think the distinction between a "block-based stream cipher" and a block cipher (or permutation) mode is the degree to which you abstract away the block cipher. Personally I wouldn't put them together. Counter mode completely abstracts away the cipher, assuming it is an idealized pseudorandom function; sponge-based modes also abstract away the permutation as ideal in most cases; stream ciphers usually do not do this, and use weaker (but still sometimes block-based) primitives to generate output. There are, for example, sponge modes that use very few rounds past the initialization, which makes them more streamy than spongy. So their cryptanalysis is often different.