I recently encounted this for googlevideo...
[xbmc@mediacenter ~]$ curl -v 'https://r6---sn-i3co-i3be.googlevideo.com/videoplayback?sv
er=3&requiressl=yes&signature=069B9F2A1C2A2119B6C3038F37BCE01AF94763F5.80B5E792FA5E0FE645
D11FAAA302842CEA047C95&itag=22&id=775731e720ecb437&upn=SgvYepNqdzc&sparams=id,ip,ipbits,i
tag,ratebypass,requiressl,source,upn,expire&mt=1393649509&mv=m&ms=au&expire=1393670156&so
urce=youtube&ratebypass=yes&ipbits=0&fexp=935610,901803,916807,916611,929305,934227,93741
7,937416,913434,936910,936913,902907&key=yt5&ip=59.148.74.80|User-Agent=Mozilla%2F5.0+%28
Windows+NT+6.2%3B+Win64%3B+x64%3B+rv%3A16.0.1%29+Gecko%2F20121011+Firefox%2F16.0.1'
* Hostname was NOT found in DNS cache
* Trying 61.238.239.17...
* Connected to r6---sn-i3co-i3be.googlevideo.com (61.238.239.17) port 443 (#0)
* successfully set certificate verify locations:
* CAfile: /etc/ssl/certs/ca-certificates.crt
  CApath: none
* SSLv3, TLS handshake, Client hello (1):
* SSLv3, TLS alert, Server hello (2):
* error:14077410:SSL routines:SSL23_GET_SERVER_HELLO:sslv3 alert handshake failure
* Closing connection 0
curl: (35) error:14077410:SSL routines:SSL23_GET_SERVER_HELLO:sslv3 alert handshake failure

---
** [bugs:#1329] curl: (35) Unknown SSL protocol error on libcurl/7.35.0**
**Status:** open-confirmed
**Created:** Wed Jan 29, 2014 05:07 PM UTC by S Adrian
**Last Updated:** Wed Feb 05, 2014 09:55 AM UTC
**Owner:** Daniel Stenberg
$ curl https://www.lynda.com/ -v
Hostname was NOT found in DNS cache
Trying 69.20.127.243...
Connected to www.lynda.com (69.20.127.243) port 443 (#0)
successfully set certificate verify locations:
CAfile: none
CApath: /etc/ssl/certs SSLv3, TLS handshake, Client hello (1):
Unknown SSL protocol error in connection to www.lynda.com:443 
Closing connection 0
curl: (35) Unknown SSL protocol error in connection to www.lynda.com:443
$ curl -V
curl 7.27.0 (x86_64-unknown-linux-gnu) libcurl/7.35.0 OpenSSL/1.0.1f zlib/1.2.8 librtmp/2.3
Protocols: dict file ftp ftps gopher http https imap imaps pop3 pop3s rtmp rtsp smtp smtps telnet tftp 
Features: AsynchDNS IPv6 Largefile NTLM NTLM_WB SSL libz TLS-SRP
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