If I have a web crawler (using a non-patched version of OpenSSL) that can be coaxed to connect to an evil https-site, can they get everything from my process memory? To attack a server you can keep reconnecting to get more 64kb blocks (if I understand correctly), but can a client be forced to reconnect many times, to get more blocks?
Yes, clients are vulnerable to attack.
The initial security notices indicated that a malicious server can use the Heartbleed vulnerability to compromise an affected client. Sources below (all emphasis is mine).
Since then, proof of concept attacks have validated this position - it is utterly certain that clients running apps that use OpenSSL for TLS connections may be vulnerable.
Note that some of these programs do not use OpenSSL. For example, curl can be built with Mozilla NSS and Exim can be built with GnuTLS (as is done on Debian).
Other common clients:
Yes it affects clients as severly, as stated on the heartbleed website:
Of course, and this is not just the case for this vulnerability or for a particular client, the client still has to initiate the connection to be attacked. In no way this vulnerability allows an attacker to initiate a connection to your web crawler and exploit the vulnerability.
In your case however, as you have a direct control over the OpenSSL client code (and I suppose this is the case based on your post), you want to ensure that your version of OpenSSL doesn't come with the Heartbeat option, and if it does, to remove it. In order to do so, you can:
Once this is done, or if your version of OpenSSL didn't include it initially, then you are not vulnerable.
Edit: Another method is to retrieve your OpenSSL version with:
And compare it to the list of affected versions available on heartbleed :