Burp Suite is described as 'integrated platform for performing security testing of web applications'. There are more than 10 alternatives to Burp Suite for a variety of platforms, including Windows, Linux, Mac, Online / Web-based and iPhone. The best alternative is Fiddler, which is free. Other great apps like Burp Suite are mitmproxy (Free, Open Source), OWASP Zed Attack Proxy (ZAP) (Free, Open Source), Charles (Paid) and w3af (Free, Open Source).
Fiddler is a Web Debugging Proxy which logs all HTTP(S) traffic between your computer and the Internet. Fiddler allows you to inspect all HTTP(S) traffic, set breakpoints, and "fiddle" with incoming or outgoing data.
Charles is an HTTP proxy / HTTP monitor / Reverse Proxy that enables a developer to view all of the HTTP and SSL / HTTPS traffic between their machine and the Internet. This includes requests, responses and the HTTP headers (which contain the cookies and caching information).