I realise hats are a doddle for experienced crocheters who can obviously just go ahead a make one without a pattern, but these are great for beginners and also anyone else who just wants to get on with it with no thinking involved!
A few general points, things I have learned along the way...
1. Avoid bright colours and patterns which can attract attention and affect the safety of the homeless person.
2. Solid colours are best. For a couple of my hats I made the edging in a different colour, but only as I ran out of yarn. In hindsight it's probably best avoided I think.
3. For the same reason, avoid 'whacky' designs and stick to plain and conservative.
4. Use dark or earthy colours which won't show the dirt (the pic above shows some of the hats lighter in colour than they are in reality!)
So here's my round-up. For each pattern I've given the link to its Ravelry page, from where you can click through to the written pattern for the hat. I've done this because I always find it useful to look at the Ravelry 'projects' to see what other people do with the pattern. All the patterns are free and have US terminology.
Patterns using worsted weight/ aran:
Basic Men's Hat by Rebecca Langford. A great basic pattern which was actually designed with the homeless in mind.
Basic Half Double Crochet Hat by Oombawka Design. Similar to the one above, and again a very useful pattern with different sizes. Personally I found the largest size massive and for most purposes I think the two smaller adult sizes would be fine.
Pompom Hat by Caron Design. I absolutely love this pattern and would have made more in this design, but sadly didn't have enough yarn in any one colour. It's a yarn eater with that lovely thick ribbed edge which folds over, but well worth making as I think it'll be lovely and warm. I omitted the pompom on mine as I thought it best to keep it simple.
Men's Hat by Jayna Grassel. Lovely pattern, only the maths didn't work out for me with the stitch increases (could be me!)... however a couple of the Ravelry projects have tweaks which might be helpful. I really love the ribbed edging and ended up using it on other hats.
Patterns using super bulky/ extra chunky weight yarn:
Truffle Shuffle Skully by Alia Smith. Loved this pattern and think it'll be another very warm one. I made two. One as written and the other with a turn up to make it look like a fisherman's hat. I just made the initial chain longer for the one with the turn up (23ch instead of 19). You could also make this with bulky/chunky yarn, using a 6mm or 6.5mm hook and changing the number of stitches in the starting chain accordingly to get the right height.
Crocheted Hat with Stripes by Drops Design. I made mine in a solid colour for the reasons mentioned, and carried on until it was long enough for a turn up. Another good basic pattern.
Patterns using DK. (Generally not advisable for extremely cold weather, but would be fine for Autumn/Spring and I had a lot of DK in my stash so thought I might as well...)
Simple Manly Hat by Mandie Williams. Came out rather on the large size with the hook recommended, so I'd go down a size or two if making it again.
Cosy Autumn Hat by Angela Scott. Nice knit-look ribbed design which will help give it more warmth.
The science of a hat pattern is really not complicated. The principle of a basic beanie pattern is a flat circle made by increasing regularly each round, then when the circle is big enough (depending on the eventual size of the hat), stop increasing and work the same number of stitches each round until the hat is the desired height. For a really handy chart, head over to this page on Annie's Picture Perfect blog where you will find instructions for properly sizing crochet hats. It's an invaluable resource.
I'd love to know if you try any of these patterns and what you think of them. Also if you've found any other suitable hat patterns, please do let me know by commenting below.