My experience is the more expensive the hotel then the more expensive the Internet which also generally means the cheaper the hotel the more likely the internet is free. And generally the hotels that charge you will charge you a fortune!
You also need to consider what a hotel means when they say Internet Access:
My experience is the hotel staff knows very little about the internet and likely cannot help you at all, you’re better off asking another person that you might see accessing the network. So if you’re not used to using your laptop on the go, don’t count on much help; get some practice at the local coffee house before you go.
Speed at hotels will vary in my experience, but it’s generally fast enough, especially if it’s free. If it’s free and in my room I can generally live with just about any speed since I can just leave my laptop connected and it’ll eventually pull it down even if it is slow.
Something I’ve seen at some access points is they block some of the ports related to sending e-mail from to your computer. They do this so people don’t send spam (I guess) but sometimes you can get around this by changing to some secure (or other obscure) ports; you’ll need to check with you’re e-mail provider in advance. Occasionally, I’ve had some problems getting mail but that’s a little rarer. I can always access my e-mail provider via the web to get my mail.
In the United States, Hampton Inns have given me the best results in having free Internet in the rooms and in the lobby (and where you get your free breakfast).
In Egypt, while internet cafes are everywhere, it’s always more convenient in the hotel. One hotel (although I think it was more the town) offered free dial-in access to the internet. This was at the (inexpensive) rate of a local phone call. Yes it was slow but since much of my work can be done off line due to software clients that I use (for mail, blogging, photos) I could write my mail on the computer before connecting, the same for blog posts and sorting photos. Once I was on-line I could click send receive for my mail, click ‘post’ for a few blog entries and hit upload for my photos and it would take care of it. It took an hour, but I didn’t sit there, it took care of it while I was gone. When I came back, all was uploaded and new mail was on the computer, it was slow but it didn’t take any time out of my day and I didn’t have to drag my laptop anywhere.