If you want a lossless format, you're already using the most "widely accepted" format. However, lossless formats are not generally widely supported.
Before chasing after lossless formats on a portable player, you should consider if you really need it. If you were to purchase a flash based player, which have capacities up to 8GB now, then that's roughly 20 albums (in FLAC). If you want more than this, you're into hard-disc based players (which already limits your options greatly), where more disc access = drain on battery life. This is what lead me to choose 160kbps VBR AAC for my iPod. (Besides disc-space requirements, AAC is a more efficient encoder and, on the iPod, decoder than MP3.)
If you still want lossless:
If you were to look in terms of number of units, Apple's iPod is not only the most abundant portable music player, it's also the most abundant player that supports a lossless audio format: ALAC (Apple Lossless Audio Codec/Coding). While Apple call it this, it isn't Apple's at all — much like AAC, it's MPEG4 lossless (so in theory, it's industry standard).
Otherwise, there are Cowon players that support FLAC. In fact, the list of players which support FLAC is on the FLAC web page
, and it's not particularly long.
As drayon suggested, you can try Rockbox, but the player will become unsupported by the manufacturer, and if you install it on an iPod, you'll find the battery life at least halves (as it's not properly optimised for the iPod's processor).