I'm a big fan of OS online maps. For walks in areas I've not visited before, I plot routes on my PC to copy to my handheld GPS. And like some others, I make good use of Google Maps and Street View to get clues about all sorts of things: whether a footpath looks accessible, whether a road looks dangerous, etc., and to find a car park to start from.
I have to say though that (for me) how I plan a walk depends very much on the region. I've found that getting from A to B (and perhaps back again) in open access areas, such as national parks and/or Scottish highlands and islands, is very different from working out routes in areas like Kent. I find the former far more straightforward!
The reason seems obvious to me. On open access moorland, boggy marshes, hills and mountains, I'll follow a route that looks promising (usually having previously read about the terrain, etc.) - actual paths might not exist and are optional if they do. However, in rural Kent (for example), working out a route can be like finding a way through a maze - with all sorts of obstacles! There might be many ways to get from A to B but I'll usually need to connect a good many rights of way, be they footpaths, bridleways or whatever, to do it. I'll almost never have the luxury of choosing the easiest or most direct route.
The benefit of carrying a GPS has been raised; I find mine invaluable! I walk in woodland a lot (not the pine plantations of neat lines!) where paths twist and turn and branch and aren't where they're supposed to be - or are where they're not supposed to be! I'm suddenly faced with a three-way fork with no idea which is the path I'd planned to take. So I choose one and check my GPS, and within a few yards I can see if I've chosen correctly.