I've googled this problem and the solution is always to forward ports, but I've actually done this and people are still unable to join my games.
I've run command prompt, checked IPConfig to determine my PCs local IP on the network, accessed the NAT forwarding section of my router's setup page, entered the proper ports (6112 - 6119 both UDP and TCP) and of course entered my computer's local IP on the network.
Now, normally I would say that this was because my upload speed is pretty poor, but seeing that this game is from the days of dialup, I shouldn't have a problem. I've had no trouble hosting a 4 player game of Rainbow Six Vegas which is a bit more bandwith intensive than Diablo 1, I'm sure, so I can't immagine what I'm doing wrong.
I've "allowed" Diablo in the Windows 7 firewall. I also tried disabling "SPI Firewall" on the router config page.
Should I try UPnP?
At this point I'm pretty much out of ideas and I'm almost positive I've done everything correctly. I'm using Windows 7 x64, but I've also tried running Diablo in Windows XP SP3 compatibility mode with no luck.