My gripe with steam is the question whether I can still register/play my steamified retail games a few years down the line. Valve may drop support, Valve may be taken over by another company, etc, etc. Promises to deliver a patch that dismantles the online registration requirement should such an event occur have been made, but a promise is still only a promise. Though the same question can be asked with any other online registration scheme, so it's not even a Steam-specific gripe.
Another thing that is a major annoyance for me with steam is that it just refuses to remember whether you've set a game to "update automatically" yes/no. It always resets back to the default enabled automatic updates when steam is (re-)launched. Another annoyance with regards to those updates is that steam will only update to the latest patch. There are valid reasons why always updating to the latest patch may not be beneficial. Mod incompatibility for example, or for example to wait a little while before applying a patch using your fellow gamers as guinea pigs to verify if a patch doesn't "break" the game.
Though, as far as the above are concerned, there are cracks and manual updates available for nearly every Steam game. So if the need arises I could always revert to those. Even though I don't think I should need to as an honest paying customer.
That said, Steam does work decently. It's certainly the lesser of evils imho. I have thus far never decided not to buy a retail game just because it has been steamified, if I want to play a game and I think it's worth the cash I'll buy it nonetheless.
And no, except for a few indie games I have never bought games directly off Steam. I still prefer my games retail.
I later found out that you CAN run in offline mode. I try to remember to put it in offline mode at the end of each play period. Reason being: if you want to play and for some reason your internet is down, you cannot play because you have to get INTO Steam to put it in offline mode. Caused my son to miss out on a week of playing all his Steam games when he moved into a new place and had no internet.
^That's nonsense^.

If Steam tries to connect to the Steam servers when you launch it, but the connection attempt fails due to for example there being no internet connection, then it will automatically give you the option to launch Steam in off-line mode. Just give it some time (a few seconds usually) to stop trying to connect to the servers, and the option to start it in off-line mode will
alwaysshow. If you don't get that option then there's obviously something wrong with the system, not necessarily with steam.
The only time an internet connection is required is for registration. Meaning: initial registration, and in many cases periodic (few months interval afaik) follow-up registration verifications. Other than that an internet connection is not needed, steam should always work in offline mode, and always offer to start in offline mode if online mode is impossible. I haven't seen it behave differently anywhere.