I have used skype for a long time in Linux.
I recently installed Suse 10.1 32 bit on a computer that was running Suse 10.0. When I boot into 10.0 Skype works fine.
I installed skype via rpm on the 10.1 suse and I get a loud high pitched tone whenever I connect to anything. Echo123 or skypeout phone.
I am running alsa:
I don't know what is different from when I boot into 10.0 and use alsa.
lsmod | grep snd
snd_seq_oss 33408 0
snd_seq_dummy 7556 0
snd_pcm_oss 47104 0
snd_mixer_oss 20480 1 snd_pcm_oss
snd_seq_midi 12928 0
snd_emu10k1_synth 11520 0
snd_emux_synth 36736 1 snd_emu10k1_synth
snd_seq_virmidi 10752 1 snd_emux_synth
snd_seq_midi_event 10752 3 snd_seq_oss,snd_seq_midi,snd_seq_virmidi
snd_seq_midi_emul 9984 1 snd_emux_synth
snd_seq 53360 9 snd_seq_oss,snd_seq_dummy,snd_seq_midi,snd_emux_synth,snd_seq_virmidi,snd_seq_midi_event,snd_seq_midi_emul
snd_emu10k1 110596 2 snd_emu10k1_synth
snd_rawmidi 28160 3 snd_seq_midi,snd_seq_virmidi,snd_emu10k1
snd_ac97_codec 87072 1 snd_emu10k1
snd_ac97_bus 6144 1 snd_ac97_codec
snd_pcm 86788 3 snd_pcm_oss,snd_emu10k1,snd_ac97_codec
snd_seq_device 11916 8 snd_seq_oss,snd_seq_dummy,snd_seq_midi,snd_emu10k1_synth,snd_emux_synth,snd_seq,snd_emu10k1,snd_rawmidi
snd_timer 25860 3 snd_seq,snd_emu10k1,snd_pcm
snd_page_alloc 13576 2 snd_emu10k1,snd_pcm
snd_util_mem 8704 2 snd_emux_synth,snd_emu10k1
snd_hwdep 12804 2 snd_emux_synth,snd_emu10k1
snd 57092 20 snd_seq_oss,snd_seq_dummy,snd_pcm_oss,snd_mixer_oss,snd_seq_midi,snd_emu10k1_synth,snd_emux_synth,snd_seq_virmidi,snd_seq_midi_emul,snd_seq,snd_emu10k1,snd_rawmidi,snd_ac97_codec,snd_pcm,snd_seq_device,snd_timer,snd_util_mem,snd_hwdep
soundcore 13024 1 snd

You might have a feedback loop... Try to adjust your settings of your microphone down (or turn of the mic-boost).

Gotta love the Linux community!
I found the mic boost was on in kmix. I switched it off and Skype worked properly but my volume was very low. I turned on mic boost (+20db) and it worked perfectly. I restarted Skype with mic boost on and it has continued to work fine without a feedback tone and with proper volume????
I'm happy.

you mustn't have your mic input played back on speaker/hph!!!

disable the (usually green) playback-button for your mic in kmixer.
mic is supposed to go direction outside->computer (record), whereas speaker should play sounds from any program (pc->outside).
enabling mic INPUT as a source for OUTPUT allmost certainly shields problems.

generally "red button on" -> "green button OFF" (except you use an E-guitar and want to hear in speaker what you're playing&recording).
adjust your mic level slider with sth like krecord using the meter display to have peaks of arround -10dB to -3dB

j