I have bought a DVD Player from LG Electronics. The only problem is that it doesn't support gapless MP3 playback. Is there a MP3 player which supports that feature (I think it's quite difficult to implement this)...

I don't think there are any. It's not that difficult but I think most manufactors don't care - mp3 playback is not even the most prominent feature of a DVD player...

Even most dedicated hardware mp3-players don't do gapless playback (very few do - like Rio's Karma).

But aren't there DVD players which play Ogg Vorbis? Gapless Playbackis a special feature of Ogg Vorbis (at least it's a native one). Do these Players support gapless playback (of MP3s or oggs)?

I did a search for DVD players that play OGG files, I have had no experience with any of them. Most of the DVD players that were brought up are off brands (Yamada, Roadstar, Buffalo Technology, etc.). As far as I can tell, mainstream DVD players that you can purchase at electronics stores don't support gapless playback of mp3 files let alone play ogg files. Most of them just play mp3 and wma files, I have yet to come across a DVD player that plays mpeg-4 AAC (yet have seen 5 car CD decks that support mpeg-4 AAC). Hopefully someone that has a DVD player that supports OGG will come in with a comment.

Doesn't mean they'd play it gaplessly. My dedicated portable unit played mp3 and Vorbis with gaps until the Rockbox firmware became usable on it. Sadly it seems most companies and consumers don't care about gapless playback so it just doesn't happen.