It seems like it's getting harder to find solid state flash-based MP3 players that also include line-in recording capability. Recent posts on the AM DX email lists have focused on the iRiver models (see my posting on the T30). One unit I have used for portable DX recording is the Samsung YP-MT6. It is very small (less than 1" square, and 2.5" long), barely larger than the AA battery that powers it.
On the side of the unit there is a very nice LCD display with bright backlighting, and the controls (multi-functional, as on most electronics today) are easy to master. The unit features a built-in mic, handy for making field recordings, and a line-in encoding jack (which is unfortunately a small 2.5 mm size plug, not the standard 1/8 inch mini plug one would expect) means you can connect it to a radio for portable recording (I'd recommend using an attenuation cable if the line out of the radio causes overloaded recordings). It also has an FM receiver which, while not super-sensitive, will pick up most local stations in stereo or mono. One very nice feature is the ability to record what's heard on the FM tuner to the player's memory as an MP3 file. That makes it a lot of fun for recording FM stations while travelling. Finally, the unit can be connected to a computer via USB and the recordings transfered as it they were on a memory stick.
Oh yes, it also plays MP3 files quite nicely.
Check eBay, they tend to run in the $15-30 range for 512MB and 1GB sizes.