There are two main types of proxy: HTTP and SOCKS.
An HTTP proxy can, as its name suggests, only really deal with HTTP traffic. You send it a request and it forwards it to the target page, and proxies the result back to you. All of this traffic is sent in plain-text, so it's possible to sniff and alter it. It is, however, possible to perform a HTTP CONNECT over some of these proxies, which turns the HTTP traffic into a TCP tunnel. From there, SSL can be used on that tunnel, allowing for protection against most types of sniffing attacks. Another type of HTTP proxy called an HTTPS proxy functions identically, except the entire protocol operates over HTTPS instead.
On the other side of things is SOCKS, which acts as nothing more than a tunnel. A message is sent to the proxy to create a connection to a target server, and the proxy then forwards everything between you and the server. There are three main versions of SOCKS in use today: SOCKS4, SOCKS4a, and SOCKS5. The SOCKS4a specs added the ability to pass a domain name as a target parameter, instead of an IP address, such that the proxy would perform the DNS lookup instead of the client. This helped fix problems where the client was unable to perform a DNS lookup itself, and also helped improve privacy, since it was previously possible to sniff the DNS lookup traffic from the client and identify the sites it was visiting. SOCKS5 further expanded the protocol to include IPv6 and UDP support, as well as better authentication. However, the actual SOCKS traffic is plaintext, and the client must provide its own transport security within the tunnelled connection.
In general, you should consider the use of a proxy to be at most as safe as sending the traffic yourself. You will still be sending plaintext information to the proxy (unless it's a HTTPS proxy) and that can be sniffed. Once the tunnel is created, the traffic can still be sniffed unless you're talking to the target server via HTTPS or a similar secure protocol.
An interesting case occurs when the operator of the proxy is malicious. Any plaintext traffic can be sniffed and stolen regardless, but a malicious proxy can perform active attacks. For example, it might inject content into your traffic, or redirect you to other servers. If you use HTTPS, then your privacy and safety are increased, but it may be possible for the attacker to "downgrade" or bypass the SSL by interfering with the SSL handshake. It may even return a forged certificate to you, and claim to be the target server, whilst secretly decrypting all of your traffic.
To put it very simply: proxies can be dangerous, and you should only use proxies that you trust.