Unfortunately, no free proxy service is going to work well with RapidShare, as RapidShare only allows one download at a time per IP address.
The problem is that most freely available proxies share a single IP address with 1000's to 10,000's of users, so it is highly likely that several users are trying to download from RapidShare through the proxy. This means that if you try downloading from RapidShare also with that proxy, it will see that a download is already taking place with this IP address and refuse the connection.
If you are just looking to get multiple files downloaded quickly/easily rather than hiding your IP for privacy, there are a few workarounds:
Free method: Use FreeRapid and add your list of download links. This runs in the background downloading each file one at a time and doing all the "clicking" for the waiting screens, etc. This is very effective at getting 10 to 20 downloads while leaving your PC running overnight or before heading to work.
Premium proxy: Purchase a VPN proxy, e.g. HMA's premium service. Unlike the free service, most premium proxies give you a dedicated IP address for your connection, which means that if you download from RapidShare or any other file host, you are the only one using that IP address. You can get around the waiting time between downloads just be changing IP address (i.e. disconnect and reconnect the VPN.) Depending on your VPN provider, you may be able to connect on multiple computers to run simultaneous downloads (I know HMA allows 2 simultaneous connections).
RapidPro account: If you do quite a lot of downloading from RapidShare or need your downloads quick, nothing beats getting an actual account with them. The catch here is that if you are concerned about privacy, RapidShare will obviously have more details about you than just an IP address.