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.
A buffer over-read exists in curl 7.20.0 to and including curl 7.58.0 in the RTSP+RTP handling code that allows an attacker to cause a denial of service or information leakage