I also use a RTL8188CUS based wifi dongle. It works pretty good on Raspbian Wheezy, not perfect, but pretty good.
But I still have problems with it on TinyCore. Connecting seems sometimes slow, ie it takes a while before it gets an IP address. And sometimes it will get an IP address, but I can't ping it from my PC. Strange.
And sometimes it just works fine, it's a bit intermittent.
@Roberts: I've been playing around with the udhcpc command. It seems that the -b command option works better then the -n option.
The -n option gives up after a few tries, and then quits, if it doesn't get a wifi connection. The -b option forks the udhcpc process and keeps on trying to connect in the background. This seems to work better on our "slow" raspberry devices.
Another thing I found usefull is the "-x hostname:" option. With that option I can set the hostname that will appear on the DHCP client list on my routers managament webpage.