A malicious server can use the FTP PASV response to trick curl 7.73.0 and earlier into connecting back to a given IP address and port, and this way potentially make curl extract information about services that are otherwise private and not disclosed, for example doing port scanning and service banner extractions.
A non-privileged user or program can put code and a config file in a known non-privileged path (under C:/usr/local/) that will make curl <= 7.65.1 automatically run the code (as an openssl "engine") on invocation. If that curl is invoked by a privileged user it can do anything it wants.
Curl versions 7.14.1 through 7.61.1 are vulnerable to a heap-based buffer over-read in the tool_msgs.c:voutf() function that may result in information exposure and denial of service.
Curl_smtp_escape_eob in lib/smtp.c in curl 7.54.1 to and including curl 7.60.0 has a heap-based buffer overflow that might be exploitable by an attacker who can control the data that curl transmits over SMTP with certain settings (i.e., use of a nonstandard --limit-rate argument or CURLOPT_BUFFERSIZE value).
curl version curl 7.54.1 to and including curl 7.59.0 contains a CWE-122: Heap-based Buffer Overflow vulnerability in denial of service and more that can result in curl might overflow a heap based memory buffer when closing down an FTP connection with very long server command replies.. This vulnerability appears to have been fixed in curl < 7.54.1 and curl >= 7.60.0.
curl version curl 7.20.0 to and including curl 7.59.0 contains a CWE-126: Buffer Over-read vulnerability in denial of service that can result in curl can be tricked into reading data beyond the end of a heap based buffer used to store downloaded RTSP content.. This vulnerability appears to have been fixed in curl < 7.20.0 and curl >= 7.60.0.
A buffer overflow exists in curl 7.12.3 to and including curl 7.58.0 in the FTP URL handling that allows an attacker to cause a denial of service or worse.