Music Numbers
If English isn't your first language, you may want to make your own version in your language.
And warning: These two methods can't be use simultaneously by one person... I think...

Chromatic Note Numbers:

When singing scales, rather than using Solfage (the Do Re Mi thing, which I've never really dug), I just sing the numbers one to seven for the major scale notes (with Seven shortened to Sen) and I name the non-major scale notes (the black notes in C major) to fit inbetween, thus a chromatic scale is: One, Woo, Two, Tee, Three, Four, Far, Five, Fix, Six, Sin, Sen. It really helps! What's more, "Far" is as far from One as you get and "Sin" is the note that defines jazz.... how appropriate!
It also means that you don't need to refer to Woo as "sharp one" or "flat two"... it's all perfectly enharmonic.
Whole tone scale: "One, Two, Three, Far, Fix, Sin, One"
Blues scale: "One, Tee, Four, Far, Five, Sin, One"
Pash Crush Scale: "One, Woo, Three, Far, Five, Fix, Sen, One"

When singing modes, you choose whether you wish to refer to One as the starting note or the key: For example, a dorian minor could be either:
"One, Two, Tee, Four, Five, Six, Sin, One"
"Two, Three, Four, Five, Six, Sen, One, Two"

Have fun!

Rhythm Numbers:

People use all sorts of fruit (mango, pineapple, etc) and Mexican things (Taco, Chihuahua, etc) to help feel rhythmic subdivisions, but I always find them a bit cumbersome and inflexible. And I like numbers! So here's another angle on it that I've come up with: Apart from the number names, I've carefully chosen sounds, based on the "e and a" used traditionally for semiquavers (16th notes), that are consistent and easy to say quickly (and to mouthe while breathing) with minimal tongue movement. My aim was to make them as mutable as possible (in both senses of the word!) so that they can be regrouped however necessary. The words "five", "six" and "seven" each have a few sounds that I stretch them over a few beats. I've given sample sentences, but you might hear different words and that's even better. Be your own guru!
1. One (or just "Wa" when really fast)
2. Two-wa ("Tua" or "Too ah")
3. Three-ya-na ("Three anna")
4. Four-ri-ya-na ("Foury anna")
5. Fa-ya-vi-ya-na ("Fire* vienna" (3-2)or "Fire vee anna" (2-3))
6. Si-ka-se-ni-ya-na ("Sick as any anna" (2-2-2)
or "Sick as a knee anna" (3-3))
7. Se-ve-nor-ra-ni-ya-na
("Seven or a knee anna" (2-2-3) or "Seven or any anna" (3-2-2) or "Seven or any anna" (2-3-2))

I say the number (underlined) and whisper or mouth the rest of it, allowing me to breathe.
*For people with accents that pronounce the "r" at the ends of words, (like American or Irish), "Fire" needs to be said as "Fyah".

I haven't bothered with beyond 7, as that's the last prime until 11, and you can just do the numbers of how it's grouped (and I've never known anyone to do "11 in the pulse"!) But see below**.

Here're a few exercises to show how I find this useful:
Grouping triplets in 4s (sounds like "Foury enough or Rianna for Ian a")
Group semiquavers in 5s (sounds like "Fire vee enough eye a vienna fire vee enough eye ya vienna")
Clave patterns: Normal clave: 3 3 4 2 4 "Three anna Three anna Foury anna Two a Foury anna". Rhumba clave: 3 4 3 2 4 which is helps to say like "Three anna Four-Ian-a Three anna Two a Foury anna"
Try things like grouping 7s in 5s... the fun never stops!!!

Let it sink into both your subconscious and your tongue's muscle memory, which will allow the gear shifts in your brain. And don't forget to use finger counting, airdrumming, foot tapping/stepping, body percussion, dancing etc to cement it all.

Thanks to Tania Bosak and Stephen Taberner for helping me to refine my thoughts on all this... onya!

Beyond 7, I've been playing with 8 as Eh-yi-two-a-four-ri-ya-na, 9 as Na-yi-na-two-a-four-ri-ya-na or Na-yi-na-three-ya-na-three-ya-na and 10 as Te-ni-ya-na-two-a-four-ri-ya-na or Te-ni-sa-two-a-fa-ya-vi-ya-na ("Ten is a 2 5"... ha ha!) The word Eleven makes it tricky, as it has an upbeat, but maybe E-le-ve-na-three-ya-na-four-ri-ya-na if it's a 434 grouping.