Here I study in detail the different exit numbering systems. These are not meant as exit lists; the road names are just for ease in following along. Go here for exit lists.
One striking pattern is that every radial road except the Masspike (and MA 2 which was unnumbered AFAICT) had exit 25 at 128 at first. Exits increased from downtown. Later on the numbers were changed; US 3 is the only road that hints at the former system.
Numbers in gray are interpolated and do not appear on any map I have seen. -- means an exit did not or does not exist. Numbers in parenthesis are unsigned.
All the info here (except the post-big dig list) is from before recent construction (Big Dig, US 1 Charlestown Tunnel).

NYC exit numbers

Radial roads:

Northeast Expwy

Northern Expwy

Northwest Expwy

Western Expwy

Masspike

Southwest Expwy

Fall River Expwy

Southeast Expwy/Central Artery

Belt roads:

MA 128

MA 25/I-495

Post-Big Dig exit numbers

Southeast Expwy/Central Artery
This follows the standard pattern of exit 25 at 128, and later became 2 separate systems, one for MA 3 and one as part of I-93. The Central Artery (north of the Mass Ave exit - unbuilt I-95) may have never had numbers until the current ones since it was planned for I-95. North is up.

old	new
	26	Storrow Dr
	25	Causeway St (NB)/Haymarket Sq (SB)
	24	Callahan Tunnel
	23	High St/Congress St (SB only)
	22	Atlantic Ave/Northern Ave (NB)/South Station (SB)
	21	Chinatown
	20	I-90
	19	Berkeley St (SB only, originally both ways)
14	18	Mass Ave
15	17	Berkeley St (NB only)
16	16	Andrew Sq
17	15	Columbia Rd
18	14	Morrissey Blvd (NB only)
19	13	Freeport St (NB only)
20	12	MA 3A (SB only)
21	11	Granite Ave (11B-A SB)
22	10	Squantum St (SB only)
23	9	Adams St (NB)/Bryant Ave (SB)
24	8	Furnace Brook Pkwy
25	7/20	I-93(MA 128)/MA 3 split
--	19	Burgin Pkwy
26	18	Washington St
27	17	Union St
28	16	MA 18 (16B-A SB)
29	15	Derby St
30	14	MA 228
31	13	MA 53
32	12	MA 139
33	11	MA 14
34	10	MA 3A
35	9	MA 3A
36	8	Raboth St
37	7	Cherry St
38	6	US 44 (6B-A SB)
39	5	South St
40	4	MA 3A (SB only)
41	3	Clark Rd
42	2	MA 3A
43	1	Rotary (US 6/MA 3A)

Northern Expwy
This follows the standard pattern of exit 25 at 128. Later, when I-95 was going to go thru Boston and I-93 began north of downtown, the exits were renumbered to reflect this. Now they are part of the extended I-93 numbers. North is down.

old	recent old	new
15	1	27	US 1
16	2	28	Sullivan Sq (SB only)
17	3	29	MA 28/38 (NB only)
18	4	30	MA 28/38 (SB only)
19	5	31	MA 16
20	6	32	MA 60
21	7	33	MA 28
22	8	34	MA 28 (NB only)
23	9	35	Park St (SB only)
24	10	36	Montvale Ave
25	11	37	I-95/MA 128 (25A-B)
26	12	38	MA 129
27	13	39	Concord St
28	14	40	MA 62
29	15	41	MA 125
30	16	42	Dascomb Rd
31	17	43	MA 133 (43B-A SB)
32	18	44	I-495 (44A-B)
33	19	45	River Rd
34	20	46	MA 110/113
35	21	47	Pelham St
36	22	48	MA 213

Northeast Expwy
As far as I can tell, the (incomplete) part inside 128 (now US 1) never had exit numbers. The exits north of 128 were not numbered until I-95 got one unified system. I don't think this road was even finished until the exits were renumbered; in fact the completion of I-95 may have brought about the renumbering. North is down.

	I-93
	Charlestown
	Chelsea
	Webster Ave (NB only)
	MA 16
	Sargent St (NB only)
	MA 60 (NB only because it was never finished)
UNBUILT GAP
45	I-95/MA 128 split
46	US 1 (SB only)
47	MA 114 (NB only)(47A-B)
48	Center St (SB only)
49	MA 62 (NB only)
50	US 1
51	Endicott Rd
52	Topsfield Rd
53	MA 97 (53A-B)
54	MA 133 (54A-B NB)
55	Central St
56	Scotland Rd
57	MA 113 (57A-B)
58	MA 110 (58A-B)
59	I-495 (SB only)
60	MA 286

Southwest Expwy
Originally this followed the old exit 25=MA 128 system. Recently it was renumbered as part of I-95. North is up. The proposed numbers in the first column were from the original plans; it appears the contractor that made the plans reversed the direction by mistake, so I include the ones on the plans and the reverse. Note how some exits were not built (and of course the part inside 128 wasn't). I recently added the exits on the final plan to the old exit numbers; note that anything above 128 was never built. I-95 would have continued past the SE Expwy as a third harbor tunnel.

prop	old	new
			I-93
	19		Washington St
33/17			I-695/MA C28
32/18	20		MA C28/Heath St/Centre St (NB only)
31/19			Washington St
30/20	21		MA 3/28/138/Washington St (NB only)
29/21	22		Canterbury St/Cummins Hwy
28/22	23		West St
27/23			Dana Ave
26/24	24		MA 135
25/25	25	12	MA 128 (I-93/I-95)
24/26	26	11	Neponset St (11A-B)
23/27	27	10	Coney St (SB only)
23/27	28	9	US 1
22/28	29	8	Main St/Mechanic St
21/29			Cocasset St
20/30	30	7	MA 140 (7A-B)
19/31			MA 106
18/32	31	6	I-495 (6A-B)
17/33			MA 152
16/34	32	5	TO MA 152
15/35	33	4	I-295
14/36	34	3	MA 123 (3B-A SB)
13/37	35	2	MA 1A (2A-B)
12/38	36	1	US 1 (SB only)

Masspike
This has always followed the same sequential system starting in west MA. East is down. Exits 20 and west were originally named; names were not unique. One official Masspike map gave exit numbers to a couple exits along I-93 (Central Artery) towards downtown; these were probably never signed, just as exit 24 was probably never signed.

1	West Stockbridge (WB only)
2	Lee
3	Westfield
4	West Springfield
5	Chicopee
6	Chicopee
7	Ludlow
8	Palmer
9	Sturbridge
10	Auburn
10A	MA 146/US 20
11	Millbury
11A	I-495
12	Framingham
13	Framingham (Natick)
14	Weston (& Newton) (EB only)
15	Weston (Boston Extension) (WB only)
16	West Newton (WB only)
17	Newton Corner
18	Boston (Allston Area) (EB only)
(19)	Boston (Allston Area) (toll plaza)
20	Boston (Allston Area) (WB only)
(21)	(onramp WB from Mass Ave)
22	Prudential Ctr/Copley Sq (EB only)
(23)	(onramp WB from Arlington St)
(24)	I-93/MA 3
(25)	(onramp WB from Congress St)
(26)	(onramp WB from High St)
(27)	(onramp WB from Cross St)

MA 2
I don't think MA 2 had exit numbers until recently, but I give what they would have been. Now the exit numbers are aligned with the rest of MA 2, even though the freeway is discontinuous. East is up.

old	new
17	60	Lake St
18	59	MA 60
19	58	Park Ave
20	57	Wollaston Ave
21	56	MA 4/225
22	55	Pleasant St (EB only)
23	54	Waltham St (WB only)(54B-A)
24	53	Spring St (EB only)
25	52	MA 128/I-95 (52A-B)

US 3
US 3 has never been renumbered; it still follows the old exit 25=MA 128 system, and is the only road to do so. North is down.

25	I-95/MA 128
26	MA 62
27	Concord Rd
28	Treble Rd
29	MA 129
30	I-495 (30A-B)
31	MA 110 (31A-B NB)
32	MA 4
33	MA 40
34	Westford Rd
35	MA 113
36	Middlesex Rd (NB only)

MA 24
MA 24 used the standard exit 25=MA 128 system, but was renumbered because it was numbered north to south, the opposite of the current standards. North is up.

old	new
44	1	MA 81 (1A-B)
43	2	Brayton Ave
42	3	I-195
41	4	I-195
40	5	TO US 6
39	6	Wilson Rd (SB only)
38	7	MA 79 (SB only)
37	8	Main St
36	9	MA 79
35	10	Main St
34	11	Padelford St
33	12	MA 140
32	13	US 44 (13A-B)
31A	14	I-495 (14A-B)
31	15	MA 104
30	16	MA 106 (16A-B)
29	17	MA 123 (17A-B)
28	18	MA 27 (18A-B)
27	19	Harrison Blvd (19A-B)
26	20	MA 139 (20A-B)
25	21	MA 128/I-93

MA 128
MA 128 was orignally numbered from Gloucester counterclockwise to Braintree. At first it used separate exit numbers for each direction in a cloverleaf; that was changed a while ago. The first exit is exit 9; that part probably wasn't the first to be built so a guess had to be made somewhere. The section east of Peabody still carries the old numbers. The other sections (I-95 and I-93) now carry the numbers of those roads. Counterclockwise is down.

old old	old	new
	9		light (MA 127)
	10		rotary (Rockport Rd)
1	11		rotary (MA 127)
2	12		Crafts Rd
3	13		Concord Rd
4	14		MA 133
5	15		School St
6	16		Pine St
7	17		Grapevine Rd
8	18		MA 22
9	19		Brimbal Ave
10/11	20		MA 1A (20A-B)
	21		Trask Ln
12/13	22		MA 62 (22B-A NB)
14/15	23		MA 35 (23A-B)
15A	24		Endicott St
16/17	25		MA 114 (25A-B)
18	26		Lowell St (26B-A NB)
	--	28	Centennial Park
	--	45	I-95
19/20	30	44	US 1 (44A-B NB)
21	31	43	Walnut St
22	32	42	Salem St
23	33	41	Main St
24/25	34	40	MA 129
26	35	39	North Ave
27/28	36	38	MA 28 (38A-B)
28A/B	37	37	I-93 (37A-B)
29	38	36	Washington St
30/31	39	35	MA 38
32	40	34	Winn St (34A-B)
33/34	41	33	US 3/MA 3A (33A-B)
35	42	32B	Middlesex Tpk
35A	43	32A	US 3
36/37	44	31	MA 4/225 (31A-B)
38/39	45	30	MA 2A (30A-B)
40/41	46	29	MA 2 (29A-B)
42	47	28	Trapelo Rd (28A-B NB)
42A	48	27	Winter St/Totten Pond Rd (27A-B)
43/44	49	26	US 20
46A	50	25	I-90
45/46	51	24	MA 30
47	52	23	Recreation Rd (NB only)
48	53	22	Grove St
49/50	54	21	MA 16 (21B-A SB)
51/52	55	20	MA 9 (20A-B)
53/54	56	19	Highland Ave (19A-B)
54A	57	18	Great Plain Ave
55	58	17	MA 135
55A/B	59	16	MA 109 (16A-B)
56/57	60	15	US 1/TO MA 1A (15A-B)
58	61	14	East St/Canton St
59	62	13	University Ave
	63	12/1	I-95/I-93 split
60/61	64	2	MA 138 (2A-B)
62	65	3	Ponkapoag Tr
63	66	4	MA 24
64/65	67	5	MA 28 (5A-B)
66	68	6	MA 37
67	69	7	MA 3/I-93

MA 25/I-495
I-495 originally started from the old end at I-95; now it starts at I-195.

old	new
	2	US 6/MA 28
	1	US 6/MA 28 (exit number recently greened out)
	1	I-195
	2	MA 58
	3	MA 28
	4	MA 105
	5	MA 18
	6	US 44
	7	MA 24
	8	MA 138
	9	Bay Rd
	10	MA 123
	11	MA 140
	12	MA 140
1	13	I-95
2	14	US 1
3	15	MA 1A
4	16	King St
5	17	MA 140
6	18	MA 126
7	19	MA 109
8	20	MA 85
9	21	Main St
10	22	I-90
11	23	MA 9
12	24	US 20
13	25	I-290
14	26	MA 62
15	27	MA 117
16	28	MA 111
17	29	MA 2
18	30	MA 2A
19	31	MA 119
20	32	Boston Rd
21	33	MA 4
22	34	MA 110
23	35	US 3
24		Lowell Connector
25	37	Woburn St
26	38	MA 38
27	39	MA 133
28	40	I-93
29	41	MA 28
30	42	MA 114
31	43	Mass Ave
32	44	Sutton St
33	45	Marston St
34	46	MA 110
35	47	MA 213
36	48	MA 125
37	49	MA 110
38	50	MA 97
39	51	MA 125
40	52	MA 110
41	53	Broad St
42	54	MA 150
43	55	MA 110
44	56	I-95

Post-Big Dig
Here I attempt to show what the exits will be on the Big Dig. I have no official source for the exit numbers, so those are just a guess. The exit placement may also be wrong as the maps aren't perfect.
I-93 NB:

old	new
16	16	Andrew Sq
17		Berkeley St
18		Mass Ave
20	20	I-90
21		Chinatown
22		Atlantic Ave/Northern Ave
24	24	Callahan Tunnel
25		Causeway St
26	26	Storrow Dr
27	27	US 1
--	28	Sullivan Sq

I-93 SB:

old	new
27	--	US 1
26	26	Storrow Dr
25		Haymarket Sq
24	24	Callahan Tunnel
23	23	High St/Congress St
22	22	South Station
21		Chinatown
20	20	I-90
19		Berkeley St
18	18	Mass Ave
16		Andrew Sq

Thanks to Shawn De Cesari for a map scan.
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